In this paper, three-dimensional terminal guidance problem of a missile intercepting a maneuvering target is studied by using a composite control scheme based on finite-time control and nonlinear disturbance observer technique. The three-dimensional model is characterized by nonlinear interception geometry, which the azimuth angle and elevation angle are coupled with each other. Many existing results are studied for planar model which ignores the coupled terms of three-dimensional model. In this paper, the coupled terms of guidance system can well be solved by selecting a special Lyapunov function, and guidance laws with finite-time convergence characteristic are derived, which have the ability to track target maneuver. Based on sliding mode control method, discontinuous switching functions are involved as augmented terms to suppress the target accelerations which are regarded as unknown bounded external disturbance of guidance systems. To improve the disturbance rejection performance of guidance system, the gains of switching functions are selected to be larger than the bounds of accelerations. However, the guidance system could generate the chattering phenomenon caused by discontinuous switching functions. To handle the chattering problem, nonlinear disturbance observers are constructed to estimate the target accelerations. The estimated target accelerations are introduced into the finite-time guidance laws and used as the feedforward compensation terms to reject the actual target accelerations. This is an efficient approach to suppress the chattering phenomenon. Then, novel composite guidance laws are presented based on finite-time feedback control and disturbance feedforward compensation. Finally, simulation results on three-dimensional missile-target interception examples are provided to demonstrate the effectiveness of the proposed approaches.