Interference fringe period is a very important parameter of phase locking in scanning beam interference lithography system. The deviation between period setting value and nominal fringe period value will cause stitching error of interference fringe between adjoining scans. To get features of scanning lithography manufactured grating diffraction wavefront, according to the characteristics of step-and-scanning lithography and working principle of dynamic phase locking, the mathematical model of scanning beam interference lithography is built. According to this model, variations of printed error and lithography grating period are given. Experiments are done to verify this model. Results show that period setting error in phase locking system will cause periodic printed error. Periods of lithography grating vary with period settings. Lithography grating period is equal to period setting value with tiny period setting error. When interference beam waist radius is 0.9 mm, step over distance is 0.6 mm and fringe period is 555.6 nm, periodic printed error is less than 1 nm with period setting relative error less than 278×10-6. If the dose contrast is more than 0.9, period setting error must be controlled within 92.6×10-6. The variable range of period setting value and lithography grating period is 102.8 pm.