This study investigates the fixed-time control problem for a class of second-order nonlinear systems. Acknowledging that most existing fixed-time sliding mode controllers encounter singularity issues, this paper aims to design a non-singular fixed-time sliding mode controller. Initially, a novel fixed-time sliding mode surface incorporating a sinusoidal function is proposed. Utilizing Lyapunov stability theory, it is rigorously demonstrated that the closed-loop system achieves fixed-time stability under the proposed controller. Furthermore, improvements are introduced to the controller design to mitigate the chattering phenomenon. It is shown that the tracking error converges to a small region around zero within a fixed time. Finally, comparative simulations conducted in MATLAB confirm the effectiveness and superiority of the proposed control algorithm.