The Tb32Co68/(SiNx/Co)n films (n = 0~3) were prepared by magnetron sputtering. The magnetic anisotropy of all Tb32Co68/(SiNx/Co)n films are perpendicular to the film plane. It is found that the saturation magnetization (Ms) and perpendicular coercivity (Hc⊥ ) of the Tb32Co68/(SiNx/Co)3 film are 263 emu/cm3 and 3592 Oe, respectively. This film appears to be a promising material as a heat-assisted magnetic recording (HAMR) medium. The cross-sectional high resolution transmission electron microscope (HRTEM) images show that the interface roughness between the (SiNx/Co)n layers and TbCo layer increases as n is increased. The rough surface provides more obstacles and pinning sites that hinder the motion of the domain walls at interface between the (SiNx/Co)n layers and TbCo layer. Therefore, the Hc values are profoundly influenced by the interface roughness.