This paper presents a finite-volume based lattice Boltzmann method for simulation of full compressible flows with flexible Prandtl number. The equilibrium distribution function is replaced with circular function where all mass, momentum, and energy is equally distributed along a circle. Two different density distribution functions are newly introduced to develop lattice Boltzmann model for compressible viscous flows. The equilibrium distribution function for the evolution equations can be derived from the integration of the Lagrangian interpolation polynomial, which depends on the configurations of the lattice model in the velocity phase space. Two-dimensional compressible flows in a shock tube were investigated to verify the accuracy of the current lattice Boltzmann method. The lattice Boltzmann method based on circular function was successfully adopted to two-dimenstional unsteady simulations with strong contact discontinuities. The present lattice Boltzmann code is applied to the subsonic laminar flow over an NACA0012 airfoil, and the computed results show fair agreement with the Navier-Stokes solution. The hypersonic flow passing through a cylinder is selected as a test case to verify the performances of the current lattice Boltzmann approach. The present solver gives a reasonable agreement with the continuum-based simulation results for flows including detached normal shock wave near the leading edge. Our results imply that the replacement of the Maxwellian distribution function with circular function may be the suitable approach for the evaluation of compressible viscous flows.