Aiming at the design problem of terminal guidance law for unmanned combat aerial vehicle to intercept high-speed and highly maneuverable target with unknown acceleration and constrained overload and attack angle, the spatial kinematic model of intercepting maneuverable target in the ballistic coordinate system was established firstly. Then, the three-dimensional guidance model under the state equation was derived. Based on this model, a disturbance observer was introduced to estimate the target acceleration. Subsequently, a non-singular terminal sliding mode guidance law with attack angle constraints was designed based on the three-dimensional non-singular terminal sliding mode surface and the disturbance observer. Finally, simulation verification and comparative analysis were conducted with the proportional navigation guidance law with angle control. The results show that both guidance laws are effective, and their performance indicators have their own advantages and disadvantages under the same simulation scenario.