To intercept high-speed maneuvering targets,a three-dimensional guidance model is built taking the autopilot's dynamic characteristics into consideration. To solve the problems of the strong nonlinearity and uncertainty of the guidance model,a three-dimensional nonlinear guidance law was designed with consideration of the dynamic property of the missiles and the maneuvering of the target. Then,an extended observer was used to estimate the maneuvering acceleration of the target. The result of simulation showed that the extended observer had better performance than the sliding mode differentiator under the interference of noise. The estimated target acceleration was used in the guidance law and made it a three-dimensional nonlinear guidance law. The designed guidance law has better guidance performance than Augmented Proportional Navigation Guidance (APNG) and the other two nonlinear guidance laws for intercepting high-speed maneuvering targets.