An efficient lattice Boltzmann (LB) model relying on a hybrid recursive regularization (HRR) collision operator on D3Q19 stencil is proposed for the simulation of three-dimensional high-speed compressible flows in both subsonic and supersonic regimes. An improved thermal equilibrium distribution function on D3Q19 lattice is derived to reduce the complexity of correcting terms. A simple shock capturing scheme and an upwind biased discretization of correction terms are implemented for supersonic flows with shocks. Mass and momentum equations are recovered by an efficient streaming, collision and forcing process on D3Q19 lattice. Then a non-conservative formulation of the entropy evolution equation is used, that is solved using a finite volume method. The proposed method is assessed considering the simulation of i) 2D isentropic vortex convection, ii) 3D non-isothermal acoustic pulse, iii) 2D supersonic flow over a bump, iv) 3D shock explosion in a box, v) 2D vortex interaction with shock wave, vi) 2D laminar flows over a flat plate at Ma of 0.5, 1.0 and 1.5.