The AUSM+ (Advection Upstream Splitting Method) finite-volume scheme, which was developed in structured grids, has been extended to be used on unstructured meshes. The linear reconstruction approach using Green-Gauss gradient estimation is applied in order to obtain second order spatial accuracy. A new gradient estimation based on the weighted average of Barth and Jespersen's three point model limiter is employed to minimize the numerical oscillations around solution discontinuities. An adaptive multigrid method is used to accelerate the convergence. Finally, numerical experiments on supersonic shock reflection flow over flat plane, transonic flow over NACA0012 and RAE 2822 airfoils are calculated to validate the methodology.