Abstract: The spatial large eddy simulations of the transition process and thefull turbulence in a supersonic flat-plate boundary layer at a free-streamMach number M_\infty = 4.5 and a Reynolds number Re = 10000 arecarried out by solving the three-dimensionalcompressible Favre-filtered Navier-Stokes equations with a hybrid method of a fifth-order upwind compact difference anda sixth-order symmetric compact difference. The compact storagethird-order explicit Runge-Kutta method is applied for the time-integration. Thesub-grid scales are formulated according to the modified Smagorinskyeddy-viscosity model. Based on the linear stability theory, a pair of themost unstable oblique first mode disturbances is imposed on the inflowboundary and the evolution of flow from laminar, transition to fullturbulence, is simulated successfully. The instant and statistical parametersare obtained, and numerical results show a good agreementwith the relevant flat-plate boundary layer theory. Especially the linearand weakly nonlinear growth of disturbance, the appearance of staggered\Lambda -vortex pattern, and the evolution of \Lambda -vortex intohairpin vortex are consistent with related findings in literature.