This paper focuses on the problem of output tracking control for a class of generalised high-order uncertain nonlinear systems. Serious uncertainties are composed of unknown high-order terms, unknown nonlinear functions and the signal to be tracked. The new feedback scheme guarantees that the tracking error belongs to a prescribed small neighbourhood of the origin in finite time. Design procedures are presented by combining improved adding a power integrator method with the recursive construction. As an application, the control methodology is used in the tracking control of the mass-spring mechanical system.