The dynamics of a two-dimensional active polymer composed of an active Brownian particle (ABP) at the head and a passive polymer chain is investigated using Langevin dynamics simulation. The ABP experiences a self-propulsion force f_s and a resistance torque M as the passive polymer chain is bonded to the edge of the ABP. M restricts the rotation of the ABP, and thus the dynamics of the ABP and that of the whole active polymer are influenced significantly. Due to this restriction, the persistence time τ_r, which characterizes the random rotation of the ABP, is increased significantly and changes non-monotonically with the rotational friction coefficient η_r. Our simulation results show that the effect of M on the dynamics of the active polymer can be characterized mainly by the change of τ_r. Moreover, the propulsive diffusion coefficient D_P of the whole polymer chain originated from the self-propulsion force can be described by a scaling relation D_P ∝ f_s²τ_r/N²η_t² with η_t the translational friction coefficient and N the polymer length. Our results show that the diffusion is promoted by the resistance torque M and τ_r is a key factor for the diffusion of active polymers.