Phase shifting profilometry (PSP) based on crossed grating projection can acquire two orthogonal phases by a phase shifting algorithm in a specific direction (the phase shifting direction is usually controlled by a phase shifting adjustment parameter). However, this technique is sensitive to the nonlinear response of the projector-camera system and has not been studied in depth yet. In this paper, we examine the effect of the nonlinear response of the system on PSP based on crossed gratings, derive phase expressions with nonlinear errors, and analyze the reason for the phase crosstalk in two directions. On this basis, we study the active and passive correction methods for the suppression of nonlinear errors. To be specific, a double five-step PSP method based on the derived mathematical expressions is proposed to passively suppress the second-order nonlinear errors. The Gamma correction method based on statistical analysis is also studied, by which the projected crossed gratings are pre-encoded to actively offset the effect of the nonlinear errors. The two methods are compared in terms of practicality. The simulation and experimental results show that the Gamma correction method is more practical to improve measurement accuracy.