The transverse light-shift can induce non-negligible polarization error in the output signal of spin-exchange relaxation-free (SERF) co-magnetometer. In this paper, a novel method for rapid measurement of transverse light-shift based on the error of steady-state response of co-magnetometer is proposed firstly, then the sources of transverse light-shift in a compact SERF co-magnetometer is modeled and analyzed from three aspects: the non-ideal linear polarization of probe laser, the circular dichroism of the atomic spin ensembles, and the stress-induced birefringence effect of the cell wall. Furthermore, the decoupling and suppression methods of transverse light-shift based on a degree of circular polarization (DOCP) regulation scheme is presented, to realize the decoupling measurement of the transverse light-shift introduced by the whole co-magnetometer cell, and cancel it out with the non-ideal linear polarization of the probe laser. Eventually, the DOCP regulation scheme suggested in this paper achieves more than a 67% suppression ratio in transverse light-shift, and the short- and long-term performance of SERF co-magnetometer are improved due to the reduction of the coupling effect between the probe laser power and transverse field. Moreover, the measurement, decoupling and suppression methods provided in this paper also have the potential to be applied to other atomic sensors, such as the SERF magnetometers and nuclear spin co-magnetometers.