A spectral volume (SV) method for unstructured grids, recently proposed by Wang et al., is developed for solving the three-dimensional Euler and Navier-Stokes equations. In SV method, a higher order reconstruction of dependent variable is available without referring to neighboring cells. The resulting scheme is very compact, and is suitable for unstructured grid method. In this study, three-dimensional linear advective equation is first solved to numerically verify the spatial accuracy of the present SV scheme. It is shown that the formal order of spatial accuracy up to third-order is almost achieved. Then, laminar boundary layer flow over a flat plate is computed to verify developed N-S code. The SV code is parallelized using the MPI library and a preliminary calculation of inviscid flowfield over ONERA-M6 wing is made on the Earth Simulator to show the potential of the SV method for large scale computations.