The dynamical and conformational properties of the comb polymer with various rigidities of the backbone and arms in steady shear flow are studied by using a hybrid mesoscale simulation approach that combines multiparticle collision dynamics with standard molecular dynamics. First, during the process of the comb polymer undergoing periodic tumbling motion, we find that the rigidity of the arms always promotes the tumbling motion of the comb polymer, but the rigidity of the backbone shifts from hindering to promoting it with increasing the rigidity of the arms. In addition, the comb polymer transitions from vorticity tumbling to gradient tumbling with the increase in shear rate. Second, the range of variation of the end-to-end distance of the backbone and the average end-to-end distance of the arms increases with the increase in the rigidity of the arms and backbone, respectively, and the range of both changes grows with the increase in shear rate. Furthermore, as the rigidity increases, the moldability of the comb polymer decreases and the orientation angle of the comb polymer increases.