It is well accepted that stiffer polymers have higher glass transition temperatures. However, the influence of chain stiffness on the slow dynamics and dynamical heterogeneity when approaching the glass transition point is still not well understood. In this work, we investigate the influence of chain stiffness on the dynamic heterogeneity and fragility of supercooled polymer melts by using molecular dynamics simulation. The chain stiffness is tuned by varying the bending strength, and the diffusion and relaxation of polymer segments are studied. We find that the power law relation between the rescaled diffusion coefficient and the structural relaxation time does not change with changing chain stiffness, indicating similarities of glass-forming behavior of polymer melts with different chain stiffness. The dynamical heterogeneities are characterized by the non-Gaussian parameter and dynamic susceptibility, and the string-like cooperative motion is analyzed by the string-length. It is found that the non-Gaussian parameter and dynamic susceptibility characterize a different aspect of dynamical heterogeneities. Though both decreasing temperature and increasing bending strength lead to slower dynamics and growing dynamical heterogeneities, there is no simple superposition between temperature and bending strength. Our work may shed new light on the glass transition behavior of polymers with different chain stiffness.