Abstract: The optimal growth disturbance theory has been one of the main theories in recent years for studying non-modal instability phenomena in hypersonic boundary layers. This theory can be viewed as an engineering estimation of the growth of non-modal disturbances. The entire study focuses on hypersonic blunt wedge boundary layer, and employs the optimal growth disturbance theory and secondary instability analysis to investigate the non-modal instability characteristics of the blunt wedge boundary layer. The analysis reveals that no unstable modal disturbances can be found in the finite computational domains for various conditions on the flat wedge surface. However, non-modal optimal growth disturbances can acquire significant energy gains. The study also finds that the energy gain of the optimal disturbance gradually decreases with the increase in Mach number, while the wall curvature promotes the growth of the optimal disturbance. However, the spanwise wavenumber of disturbance with the maximum energy gain varies with the curvature condition, thus there is no uniform trend in curved isentropic compression surfaces. Furthermore, the study investigates the nonlinear evolution of the stationary optimal disturbance using the non-parallel parabolized stability equations and analyzes the secondary stability characteristics of the streaky boundary layer based on the linear stability theory. The results indicate that the streaky structure associated with the optimal growth has strong secondary instability, which is conducive to the transition of the downstream boundary layer to turbulence. These research findings have significant implications for the design of forced transition devices in the forebody inlets of hypersonic vehicles.