In conventional linear parameter-varying (LPV) modelling and gain scheduling control design for turbojet engines, the linearisation is performed at a set of equilibrium points, and the validity of such LPV models is ensured near the equilibria. However, the linear model can only provide an approximate description of the engine’s state when the system operates away from equilibrium. In this paper, it is suggested that such linearisation should be carried out not only at equilibrium states but also in transient (off-equilibrium) operating regimes. This will result in a global approximation to the system states whether equilibrium or off-equilibrium. Theoretically, the transient control performance can be improved by introducing such an off-equilibrium linearisation-based control procedure. Subsequently, a gain scheduling control procedure based on off-equilibrium linearisation models is proposed by using sum-of-squares (SOS) programming, which, compared with many convex programming methods, can provide less conservative results. The resulting off-equilibrium linearisation-based nonlinear control procedure with SOS programming can capture a wide range of transient engine dynamics with better accuracy, and further achieve better control performance.