It is widely accepted that the strength, deformability, and failure behaviors of rock material are strongly influenced by widespread natural fissures. Research focusing on the crack initiation, propagation, and coalescence behavior in fissured rock material is important to ensure the reliability and predictability of rock engineering. However, the types and forms of pre-existing fissures are complex and variable; thus, mechanical experiments have rarely been conducted on rock samples containing non-straight prefabricated open fissures. In this research, the strength, deformability, and failure behaviors of sandstone samples containing a single non-straight fissure were systematically investigated by a series of uniaxial compression experiments and numerical simulations. First, the influence of the fissure angle (alpha) on the strength and deformation characteristics of red sandstone containing a single non-straight fissure was evaluated. Then, the ordinary state-based peridynamics model was used to investigate the fracture behavior of red sandstone specimens with respect to various alpha values. The results indicate that for alpha = 0 degrees-15 degrees and 75 degrees-90 degrees, tensile cracks first initiated from the convex points of the prefabricated fissure, and the crack initiation position transferred from the convex point to the tip of the prefabricated fissure for alpha = 30 degrees-60 degrees. In addition, for the alpha = 0 degrees-90 degrees, the cracks initiated in the form of tensile cracks, and the ultimate failure modes were mixed tensile and shear failure. Secondary cracks always appeared in the form of shear crack. Moreover, for alpha >= 75 degrees, fewer cracks were initiated before the peak strength was reached; afterward, the crack initiations were more prolific, and more acoustic emission counts were observed.