Real-world dynamical control systems are often subject to input saturation due to the physical constraints of actuators. This causes the response performance of the system to be reduced due to the effect of input saturation. To this end, we propose a finite-time performance enhanced bounded control (FTPE-BC) method based on sliding mode control for finite time tracking of linear systems with input saturation. In this method, an approach rate based on inverse tangent function is proposed to make the system converge in finite time. A bounded controller based on sliding mode control is proposed, in which two control parameters are introduced to reduce steady-state error, settling time and overshoot. Meanwhile, the finite-time stability of the system is proved in a domain of attraction. The parameters selection principle of the controller is given to improve the transient and steady-state performance of the closed-loop system. The simulation results verify the superiority of the proposed method in the transient and steady-state performance enhancement.