In order to attain global optimal or quasioptimum solution for power transformers design, some interrelated key techniques such as encoding scheme, genetic operators, constrained condition, fitness function for the simple genetic algorithm (SGA) are further reformed and researched. An improved genetic algorithm (IGA) is developed in this paper and applied to the optimum design of S9 power transformers for the first time. In addition, a multi-objective algorithm based on IGA is applied successfully in the double objective optimum design of S9 power transformers, by using the theory of variable weight coefficients for the multi-objective optimization. All the achievements in the paper are verified by a representative mathematical example and a practical S9-1000/10 kV power transformer. All the optimization results are satisfactory and show that IGA has powerful ability of global searching, excellent solution precision and has a bright application prospect in the fields of power transformers design.