Existing methods typically used to detect transmitted wavefronts (i.e. the phase-shifting interferometer) operating at only a few specific wavelengths, to overcome this limitation and improve the accuracy of transmitted wavefront detection, a digital multi-wavelength laser interferometric system and a feedforward open-loop hysteresis nonlinearity compensation method are proposed in this paper. The laser interferometric system contains a light source system, a collimating system, an imaging system and a phase-shifting control system. The light source system contains five lasers, and five lasers are 473, 532, 632.8, 721, 1064 nm lasers, respectively. The physical table lookup analysis method is utilized as the compensation method to compensate the hysteresis nonlinearity of piezoelectric transducers. At the same time, the hysteresis nonlinearity compensation method is applied in the multi-wavelength laser interferometric system. The experimental results show that the displacement linearity error of piezoelectric transducer reaches 0.58 V and the linearity reaches 18.68% without compensation. After using the physical table lookup analysis method compensation, the maximum displacement error of piezoelectric transducer is reduced to 0.07 V and the linearity reaches 2.42% at the lookup number of 1000, which proves that the method can accurately compensate piezoelectric transducer' hysteresis nonlinearity. At the same time, the multi-wavelength laser interferometric system with the feedforward open-loop hysteresis nonlinearity compensation method is applied successfully to detect the transmitted wavefront of a glue lens at various wavelengths. The experimental results show that the maximum predicting error at 532 nm reaches 0.003 and the maximum predicting error at 632.8 nm reaches 0.002, which prove that the physical table lookup analysis method can be applied in the multi-wavelength laser interferometric system to improve the accuracy of transmitted wavefront detection and the multi-wavelength laser interferometric system has certain practicability.