A preliminary design procedure for a multi-stage axial compressor is developed, which is based on the stage-stacking method. It determines the flow coefficient which gives rise to the design conditions required such as pressure ratio, mass flow rate and rotational speed for a given specific mass flow rate at inlet to a compressor. With this flow coefficient, blade radii, every stage and compressor performance characterics such as stage pressure ratio, adiabatic efficiency etc. are calculated by stacking each stage performance characteristics. It is shown that there is an optimum number of stage which results in the maximum of compressor overall efficiency for a given specific mass flow rate at inlet to a compressor. A test design was tried for three different geometric design constraints, and comparison with a previous study shows that present procedure could be used reliably in determining the number of compressor stage in preliminary design stage.