This paper focuses on the quality improvements on clinching joints using a servo press with a Radial basis function neural network and a sliding mode (RBFS) control strategy. Bottom thickness, which is affected by the press punch position, is usually used to monitor clinching joint quality. Traditional clinching presses are driven by pneumatic pistons or motors that provide feedback on punch force or motor position. However, this feedback is indirectly related to the joint bottom thickness. Clinching workers who set the control parameters on these presses depend on tests and statistics. Thus, this paper presents a servo press system that utilizes punch position feedback to directly control the joint bottom thickness. Transmission errors are considered for the movement accuracy of the servo press. A mathematical model of the servo press is established for analyzing. An algorithm, which combines RBF neural network and sliding mode, is proposed and applied for press position tracking. This algorithm adopts an RBF neural network to approximate the nominal model of the press system. The update law of the algorithm is based on the Lyapunov function used to prove the stability of a closed-loop system. The sliding mode controller compensates for the neural network error and disturbance. Finally, experiments are executed on the servo press with an RBFS controller. To evaluate the performance of the proposed method, a fuzzy PID controller is also applied to the press for comparison. The results indicate that the servo clinching press system with RBFS efficiently and accurately control the clinching jointing process.