Self-Piercing Riveting (SPR) technique faces challenges as it expands to low ductile materials. In this paper, the ball-shaped die is suggested to prevent the formation of cracks in sheets during the SPR process. The SPR model with the ball-shaped die was developed using the finite element method, and simulations of the joint forming process and tensile test were conducted. The influence of die depth and diameter on SPR forming process and quality was analysed. The simulation results showed that as the die diameter increases, the undercut decreases, and the remaining thickness of bottom increases. The undercut and the remaining thickness of bottom decreases with the increase of the depth of the die. When employing a ball-shaped die with a 1 mm depth and 10 mm diameter, the SPR joint with tight interlock and excellent mechanical properties can be obtained. The results of the simulation and experimental tests are consistent.