This paper proposes a new extended stateobserver-based sliding mode control strategy with prescribed finite-time convergence. Firstly, a novel prescribed finite-time extended state observer is designed, which estimates the disturbance accurately within a prescribed finite time and effectively solves peaking value problem. Secondly, a new type of second-order prescribed finite-time sliding mode controller is designed to ensure system states converge within a prescribed finite time. Then, the proposed control strategy is applied to the design of partial integrated guidance and control with two-loop controller structure. Finally, the validity of the proposed methodology is verified through numerical simulation.