A numerical method using dual time stepping and preconditioning procedure for efficient computations of unsteady low speed compressible flow problems is developed. The time-derivative preconditioning method which is valid at low speed flow conditions cannot maintain temporal accuracy because of the modification of the time-derivative term in Navier-Stokes equations. The dual time stepping procedure is incorporated to enable the time accurate computations and this procedure introduces a pseudo-time derivative in addition to the physical time derivative. At a given physical time, an inner iteration can be carried out until a steady state in pseudo-time is achieved. This will effectively yield a time accurate solution. Computational capabilities of the above algorithm are demonstrated through computation of a variety of practical fluid flows and it is shown that the algorithms is efficient in the essentially incompressible flows and low Mach number compressible flows with heat source.