This paper is presented by the application of parallel adaptive evolutionary algorithm(PAEA) to search an optimal solution of a thermal unit commitment problem. The adaptive evolutionary algorithm(AEA) takes the merits of both a genetic algorithm(GA) and an evolution strategy(ES) in an adaptive manner to use the global search capability of GA and the local search capability of ES. To reduce the execution time of AEA, the developed algorithm is implemented on an parallel computer which is composed of 16 processors. To handle the constraints efficiently and to apply to Parallel adaptive evolutionary algorithm(PAEA), the states of thermal unit are represented by means of real-valued strings that display continuous terms of on/off state of generating units and are involved in their minimum up and down time constraints. And the violation of other constraints are handled by repairing operator. The procedure is applied to the $10{sim}100$ thermal unit systems, and the results show capabilities of the PAEA.