A space-marching algorithm to solve the Navier-Stokes equations on unstructured hybrid grid is proposed for supersonic viscous flows about complex configurations. The method employs a domain marching algorithm in which a band like computational subdomain, named active domain, is marched in the hyperbolic direction starting from the upstream boundary of the flow field. A masking procedure is employed where the outside of selected domain is masked during the flux computation to minimize the overall arithmetic operations. The unmasked domain is integrated in time to get a locally converged solution. The method is applied to calculations of a supersonic laminar flow past a 10 deg half angle circular cone, and a supersonic turbulent flow around a High Speed Civil Transport (HSCT) configuration. It is demonstrated that the computational work can be significantly reduced by the present method as compared to conventional time marching unstructured grid method without decreasing the solution accuracy.