An explicit cell centered finite volume CFD solver called Pyramid2D has been developed for solving Euler's equations in two dimensions. We modify the flow equations at the boundary faces, according to the physical boundary conditions, and solve them in finite difference discrete form suitable for unstructured grids. The flow properties at the cell faces are constructed using new reconstruction method which allows small oscillations at the shock wave region and in the same time contains enough diffusion, so it doesn't require the use of limiters for transonic flows. The developed solver is to be used as an external aerodynamic solver; all tests showed that the proposed scheme is robust and its numerical results compares well with the published data.