The current paper develops an effective and robust digital guidance law to intercept the highly manoeuvring target described by the continuous-time non-linear dynamic system. First, an optimal linearization model for the non-linear system is constructed at the operating point of interest on the trajectory. Then, high-gain optimal linear quadratic analogue tracker and observer are designed by utilizing the optimal linearization model and the optimal control theory, so that the effect of the unpredictable acceleration of the target can be substantially attenuated and even can be disregarded. For reducing the control effort without raising the prescribed interception time, and for practical implementation of the designed tracker, the prediction-based digital redesign method is utilized to obtain relatively low-gain digital tracker and observer from the well-designed high-gain optimal analogue tracker and observer. With the aid of the global positioning system, the proposed observer-based digital tracker is able to successfully intercept a highly manoeuvring target without the constraint on initial trajectory, and can effectively deal with various barriers during the interception. Illustrative examples are given to demonstrate the effectiveness and robustness of the proposed digital guidance law.