Aiming at the problem of impact angle constraint and input saturation, an integrated guidance and control (IGC) algorithm with impact angle constraint and input saturation is proposed. A three-channel independent design model of missile IGC with impact angle constraint is established, and an extended state observer with fast finite-time convergence is designed to estimate and compensate model errors and coupling relationship between channels. Based on the nonsingular terminal sliding mode control and backstepping control, the IGC three-channel independent design is completed. Nussbaum function and an auxiliary system are introduced to deal with the input saturation. The Lyapunov function is constructed to prove the finite-time convergence of the IGC algorithm. The missile six-degree-of-freedom simulation results show the effectiveness and superiority of the IGC algorithm.