Due to the gamma nonlinear effects of the projectors and cameras, the Direct Current(DC) component of the deformed fringe pattern and the intensity distribution of background image are not equal, so measurement errors are introduced. This paper introduces a background image correction method in the traditional 2+1 phase-shifting algorithm. The intensity distribution of the captured background image is used as a template, and the DC component of the deformed fringe pattern is approximated by the least squares principle, which can effectively improve the measurement accuracy. And the phase shift of the 2 phase-shifting sinusoidal gratings is no longer fixed to be π/2 in the new 2+1 phase-shifting algorithm, the algorithm is more flexible. The experimental results verify the effectiveness and practicability of the algorithm.