The axial compressor is one of the most challenging components in aero-engine system and design; because of that finding an optimum design for this component is very important and valuable in the field. In this study, the objective functions selected to apply optimization method are the stage efficiency which leads to minimum losses, the stall margin which allows a wide stable characteristics curve and the inlet stage specific area which is related to the weight of a stage. In any case, the weight reduction inevitably causes loss of efficiency, and the higher efficiency will lead to decrease of the surge margin. The selected design variables are mean diameter of the stage, flow coefficient, axial velocity ratio for rotor and stator, rotational speed of the shaft and the inlet flow angle. The formulated multi-objective problem is solved by using weighting method in which the multi-objective problem is converted into a single objective one. The unconstraint single objective problem is solved by using interior penalty function method with DFP (Davidson Fletcher Powell) method. A computer code has been developed and results are taken corresponding to different sets of the weightages.