Several kinetic descriptions have already been utilized for the simulation of rarefied gas mixture flows. Although such developments are important, Navier-Stokes computation can find extended use in engineering applications. Recently, the authors have derived new velocity-slip and temperature-jump boundary conditions for slip flows of gas mixtures. Appealing to these new boundary conditions, Navier-Stokes computation of rarefied gas mixture problems has become feasible.In the present contribution, the proposed conditions in conjunction with the Navier-Stokes equations and an equation for the conservation of species are solved for some binary gas mixture problems in the slip flow regime. Applications include low pressure flow in a converging-diverging nozzle, wall-cooling of a nozzle under rarefied condition, and parallel mixing in a microchannel. Simulation results are presented in terms of the distributions of overall Knudsen number, Mach number, pressure, temperature, and concentration.