This article investigates the problem of finite-time prescribed performance control for 2-D plane vehicular platoon systems with uncertain dynamics and external disturbance. First, a novel class of finite-time performance functions (FnTPFs) are designed to guarantee both spacing tracking error and bearing tracking error converge to the prescribed region within the pre-defined time with small overshoot. Then, new third-order finite-time sliding mode surfaces are designed, based on which, an improved sliding mode control scheme is established, and proved to be capable of steering the platoon tracking errors approach to small region near zero within user-defined time, while avoiding the chattering and singularity problems. Lastly, the effectiveness of the proposed scheme, together with the superiority to the existing ones, is verified by numerical simulations.