The work aims to analyze the effect of the curvature radius of workpiece, dwell time and finishing angle on material removal depth and the offset degree of material removal curve in ultrasonic assisted magnetic abrasive finishing of titanium alloy curved surface and establish material removal functions for different tool paths. Single point finishing experiments were carried out on titanium alloy curved surface under different curvature radius of workpieces, dwell time and finishing angles. The variance analysis method was used to analyze the influence of various factors on material removal depth and the offset degree of material removal curve. The material removal curves of material removal pit in xoz plane and yoz plane were fitted by the least squares method. The function expressions between the coefficient of material removal curve functions under different finishing parameters and the parameters were constructed based on quadratic polynomial stepwise regression method, and the accuracy of the function expressions was assessed. From the variance analysis of material removal depth, the F value of dwell time was equal to 8.06 and the F value of finishing angle was 2.296. The material removal depth rose with the increase of dwell time and the curvature radius of workpiece, and increased in the beginning and then decreased as the finishing angle enlarged. From the variance analysis of the offset degree of material removal curve, the F value of curvature radius of workpiece was equal to 2.176 and the F value of finishing angle was 7.647. The offset degree of material removal curve decreased as the curvature radius of workpiece increased, and rose with the increase of dwell time and finishing angle. In addition, the correlation coefficient value R2 of the fitting material removal functions was in the range of 0.97 to 0.99. The dwell time has the most significant effect on the material removal depth, the secondary is finishing angle, and the last is the curvature radius of workpiece. The finishing angle has the most significant effect on the offset degree of material removal curve, the following is the curvature radius of workpiece, and the least is dwell time. The fitting result of material removal function is very accurate and can meet the actual finishing requirements.