With the wide use of NC, higher accuracy in machining is increasingly required for premium mechanical components. However, machining accuracy is affected by many factors, especially by the way of the tool positioning and the geometry of the tool nose. This paper, based on the actual NC lathe tool and turning, generalized and abstracted the machining process by establishing the imaginary tool nose and the tool tip’s arc centre as the cutter-contact point, and analyzed systematically the influence of the factors, including the way of the tool positioning, the nose, and the tool tip’s arc radius, on the machining accuracy when machining transverse, cylindrical-surface, circular cone, quarter-circular and some surfaces can be expressed by formula etc.. Derived the error calculating formulas for turning in different surfaces. Put forward two error compensation methods, direct calculating method and enveloping method of error compensation. Experiments were carried out and results have shown that the two error compensation methods can considerably reduce the machining error in NC turning operations.