In order to realize intercept angle constraint and finite-time convergence when a missile intercepts a maneuvering target, a guidance model was proposed on the basis of the first-order missile dynamics. By regarding the target acceleration as unknown bounded external disturbance, and by applying the dynamic surface of nonlinear backstepping theory, a nonsingular sliding mode guidance law with missile dynamic was designed. Based on the Lyapunov stability theory, it was proved that the states of guidance system asymptotically converged to zero. Simulations on intercepting targets with constant maneuvering of low attitude and high velocity were made. Simulation results indicate that the designed guidance law can effectively reduce the influence caused by the missile dynamic delay, and the miss distance and the intercept angle error are small; by comparison with the optimal guidance law with missile dynamic and intercept angle constraint, the designed guidance law has higher guidance accuracy. 