An accurate, fast, matrix-free implicit method has been developed to solve the three-dimensional compressible unsteady flows on unstructured grids. A nonlinear system of equations as a result of a fully implicit temporal discretization is solved at each time step using a pseudo-time marching approach. A newly developed fast, matrix-free implicit method is then used to obtain the steady-state solution to the pseudo-time system. The developed method is applied to compute a variety of unsteady flow problems involving moving boundaries. The numerical results obtained indicate that the use of the present implicit method leads to a significant increase in performance over its explicit counterpart, while maintaining a similar memory requirement.