In single-point incremental forming (SPIF) process, a number of parameters are involved and need to be adjusted before the commencement of the forming operation. The inappropriate selection of these parameters could be detrimental to process accuracy. In this paper, the effect of five parameters, namely, sheet thickness, tool radius, step size, wall angle, and pre-straining level of sheet, on the profile accuracy of the produced part of AA1060 with SPIF is experimentally investigated. A response surface method is employed for the experimental design and regression analysis. The experimental results are presented in the form of graphical three-dimensional response surfaces. The results of ANOVA show that the sheet thickness, wall angle, step size, and the interaction between the sheet thickness and wall angle are extremely significant in terms of their effect on profile accuracy. Furthermore, an empirical model is proposed to achieve improved profile accuracy in terms of the optimized parameters.