A finite time convergent control algorithm on integrated missile guidance and control is proposed to meet the needs of intercepting maneuvering targets at high speed. Firstly, a finitetime convergent lineofsight rate model is derived based on total integrated missile guidance and control according to the traditional total integrated missile guidance and control model. Secondly, a nonlinear sliding mode switching function with compensating factor is construct, and a finite time convergent control algorithm of integrated missile guidance and control is designed based on finitetime convergent theory. Besides, an adaptive method is adopted to estimate the maximum value of the system's uncertainty, and the higherorder sliding mode differentiators are adopted to solve the higherorder derivatives of lineofsight rate and the distance between the missile and the target. Finally, the simulation results show that the proposed finite time convergent control algorithm can achieve the finite time convergence of the lineofsight rate, and has less miss distance and shorter intercepting time, compared to the general control algorithms.