Structured light system using a digital video projector is increasingly used for a 3-D shape measurement because of its digital nature. However, the nonlinear gamma of the projector causes the projected fringe patterns to be non-sinusoidal, which results in phase error therefore shape measurement error. Previous work showed that, by using a small look-up-table (LUT), this type of phase error can be reduced significantly for a three-step phase-shifting algorithm. In this research, we prove that this type of phase error compensation method is not limited to a three-step phase-shifting algorithm. It is generic for any phase-shifting algorithm. The phase error compensation algorithm is able to theoretically eliminate the phase error caused by the gamma of the projector completely. It is based on our finding that in phase domain, the phase error due to the projector's gamma is preserved for arbitrary object's surface reflectivity under arbitrary ambient light condition. The phase error can be pre-calibrated and stored into a LUT for phase error reduction. In this research, we captured a set of fringe images of a uniform flat surface board for such a calibration. The phase error of the flat board is analyzed and stored in a LUT for phase error compensation. Our experimental results show that by using this method, the measurement error can be reduced by at least 13 times for any phase-shifting algorithm.