This paper proposes a method for designing a contract model of the weather derivatives between energy utilities. They are useful for hedging the weather risks. They may be expressed as the function of the weather conditions such as the average, the maximum temperature, etc. Although the contracts existed in the past, it is not clear how to design them systematically. In this paper, an efficient method is proposed to determine a reasonable contract model of weather derivatives. It is important to select the normal data in a given data set so that a reasonable model is constructed by the learning process. This paper formulates the contract model as a two-phased problem. Phase 1 deals with data clustering to extract the normal data with DA (Deterministic Annealing) of global clustering technique. Phase 2 handles an optimization problem that equalizes the payoffs between two companies with EPSO (Evolutionary Particle Swarm Optimization) of meta-heuristics for optimizing the parameters of the contract model. The proposed method is successfully applied to the real data in Tokyo.