This paper presents a parallel multigrid method for computing inviscid and viscous high speed steady-state flows with reacting hydrocarbons. The governing equations for reactive flow are solved using an explicit multigrid algorithm while treating the chemical source terms in a point implicit manner. The CUSP (Convective Upwind and Split Pressure) scheme is used to provide necessary artificial dissipation without contaminating the solution. This explicit method yields excellent parallel speedups, thus enabling the calculation of reactive flows with detailed chemical kinetics including large numbers of species and reactions. Results indicate good multigrid speedups and adequate resolution of the reaction zone in inviscid and viscous two-dimensional hydrogen/air and methane/air test cases.