This work focuses on the ground-state phase diagram, the compensation temperatures and critical behaviors of a ferrimagnetic graphene-like trilayer induced by crystal fields and exchange couplings. The simulation results show that a negative decrease in crystal field or an increase in exchange coupling can increase critical temperature. More importantly, the M curve with double compensation temperatures can be observed, which is not predicted in the Néel theory. The remarkable compensation phenomenon has potential application value in the field of magnetic recording.