A new composite guidance law for intercepting manoeuvring targets with desired terminal line-of-sight (LOS) angle constraint is proposed in this paper. The presented guidance law is derived through generalized model predictive control (GMPC) augmented by a target manoeuvre estimator. More specifically, the target manoeuvre estimator is used to estimate and compensate for the unknown target manoeuvre online while the GMPC is used to obtain optimal LOS angle tracking performance. Stability analysis shows that the LOS angle tracking error and the LOS angular rate can converge to a sufficiently small region around zero asymptotically. The effectiveness of the proposed guidance law is validated by applying it to a surface-to-air missile for intercepting a head-on manoeuvring target under different scenarios.