Hi Kim Bye,
You need to post some pictures and give some lathe make and type information to make a proper diagnosis on your problem.
From your limited description, it appears that your metal turning lathe headstock is out of adjustment to your lathe bed ways. On some lathes this can be adjusted by loosening the headstock from the lathe bed and using the adjustment jacking bolts provided, you can bring the headstock into alignment with your lathe ways. On older or cheaper Chinese made lathes it is necessary to hand scrape the headstock to correct this type of misalignment problem and this is best left to the experienced to do.
If I were you, I would do a few checks first, before undoing or attempting to do any adjustments. Make sure that the lathe feet holding down bolts are not inducing a twist in the lathes bed. This can throw the alignment of a lathe out. There should be an even loading on each lathe foot. Loosen off the holding down bolts an try to rock the lathe. This will tell you if there is an uneven base. If rubber mounts are used, this won't be a problem, as the rubber is forgiving and will take up a certain amount of floor unevenness.
Check that the lathe spindle bearings are correctly adjusted. Loose bearings could induce errors into a lathe.
A level check over the length of the lathe should be made, to check for lathe bed twist and for general alignment. A machinist spirit level must be used to do this check. A lathe does not have to be perfectly level to cut accurately. This is apparent if you have ever used a lathe on a ship, nevertheless, for use ashore, the general practice is that a lathe should be level in both the X and Y axi over the lathes bed length.
Using a piece of steel about 250 to 300 mm long and about 25 to 30 mm diameter and put it into your 3 jaw chuck and take a light cut along its length, at least that part sticking out of the chuck, without the centre of the tailstock holding the free end. Then measure the outside diameter of the test cut and the distance that the two measurements were taken from each other. From these measurements, you can easily deduce if your headstock spindle centreline is running parallel with the lathe bed ways, or not.
To further check to see if the lathe headstock is out, using a piece of 10 or 12 mm round or square flat steel plate, as big as will fit in your lathe and mount it into a 4 jaw chuck and making sure that you will not machine into your chuck jaws, take a facing cut of the steel plate. When this is done, you can put a straight edge onto the faced surface and you will either have a concave or a convex surface, depending on the direction of out of alignment that the lathe headstock spindle centreline is in relation to the lathe ways.
The two above methods of checking "results" from doing the above, should be comparable in the amount that they are out of adjustment. If not, there are is also a problem with the cross slide ways been out of square, with the lathe bed ways. But that is not for this test, just yet. This test is just to see if you are getting similar readings in the amount of error.
Only then should you consider adjusting the headstock. If you are not comfortable with adjusting the headstock yourself, ask a machinist or an experienced friend to help you. The process will require adjustment, test cut, measurements and again adjustment, test cut and measurements, until you are bang on. This is not something I do without plenty of time. Its taken me up to a day to get a lathe into an acceptable accuracy, in the past.
After that you will have to readjust the lathes tailstock centres. To do this, put a lathe centre into the headstock spindle bore. Drill two centre holes in your newly created test bar and mount it between centres and take a light cut over the entire length of the test bar. Measure the diameters of the test cut , divide by two and using a dial gauge mounted on the lathe bed, adjust the tailstock. Repeat this process until your test bar reads the same on both ends.
I hope that this long winded explanation help you understand your lathe better. Geoffrey.
I`ll try all the tweaks and see where that gets me.