Numerical optimization with multiple objectives is carried out for design of an axial compressor blade. Two conflicting objectives, total pressure ratio and adiabatic efficiency, are optimized with three design variables concerning sweep, lean and skew of blade stacking line. Single objective optimizations have been also performed. At the data points generated by D-optimal design, the objectives are calculated by three-dimensional Reynolds-averaged Navier-Stokes analysis. A second-order polynomial based response surface model is generated, and the optimal point is searched by sequential quadratic programming method for single objective optimization. Elitist non-dominated sorting of genetic algorithm (NSGA-II) with ${varepsilon}$-constraint local search strategy is used for multi-objective optimization. Both objective function values are found to be improved as compared to the reference one by multi-objective optimization. The flow analysis results show the mechanism for the improvement of blade performance.