This paper presents the development of a numerical algorithm for the computation of axial thrust load on a centrifugal compressor. An unstructured flow solver has been developed for the computation of a hybrid, structured and unstructured grid. The computational domain of the impeller has been discretized using a structured mesh, while the computational domain on the back side of the wheel has been discretized using an unstructured mesh. The two grids are merged and a median dual-mesh is generated. The Navier-Stokes equations are discretized using a finite volume method. Roes flux-difference scheme is used for inviscid fluxes and directional derivatives along edges are used for viscous fluxes. The gradients at the mesh vertices are calculated using the Least-squares method. An explicit scheme is used for time integration. Convergence is accelerated using a local time-step and implicit residual smoothing. The results of the numerical simulation include the axial thrust load of the centrifugal compressor. In addition, details of the leakage flow are presented.