A method for selecting the optimum principal dimensions of a centrifugal impeller (under a specified set of constraints) is described. The proposed procedure is based on maximizing the overall isentropic efficiency for a given set of design requirements (mass flow rate and pressure ratio). Numerical optimization technique, for solving non-linear programming problems, has been used to solve a design objective function. The results have shown that a quicker and more accurate estimation of impeller overall dimensions is achieved. Furthermore, it should not be difficult to re-structure the proposed program so that the preliminary optimization of the complete stage might be carried out.