This paper presents a study of Smith-Purcell (SP) radiation properties with the particle-in-cell (PIC) simulation. The model supposes one-dimension (1D) dielectric cylindrical photonic crystal driven by a single electron bunch and a train of periodic bunches, respectively. The results show that the radiation from a single electron bunch is enhanced by increasing the dielectric constant and layers of the photonic crystal. The terahertz (THz) coherent SP radiation is obtained by exciting the photonic crystal with periodic electron bunches. The coherent radiation strength is improved by choosing proper operating parameters.