Lattice Boltzmann Method (LBM) has developed as a new method in the field of Computational Fluid Dynamics and is a good alternative to the conventional numerical techniques like Finite Difference (FDM) and Finite Volume Method (FVM). The aim of this research work is to develop a novel robust FVM-LBM computational solver for compressible flows. The LBM model proposed by Kataoka and Tsutahara has been implemented in the new hybrid method which has been benchmarked for the following standard problems: shock tube problem (1D), shock expansion problem (2D), Roe Test and Riemann problem. The hybrid method has a higher computational efficiency and the results obtained with this method gives a steeper and more accurate shock profile as compared to the ones obtained by the FVM along with the widely used Godunov scheme. Finally, a thermodynamically consistent and fully conservative model for multi-component flows has been discussed and benchmarked for a few test cases. The new hybrid method has been used to simulate fluid flow having gases with different ratio of specific heat and molecular mass. It has been also observed that the hybrid method is more efficient than the pure FVM for multi-fluid flows.