Power transformer dissolved gases concentrations have characteristics of single-peak. So, improved Gray Verhulst model was proposed in this paper and introduced into Power transformer dissolved gases concentrations prediction. Improved Gray Verhulst model used background function parameter ?? instead of 0.5 in the background function of original Gray Verhulst model. There are two selection rules of background function parameter ??, one is prediction error method, the another is posteriori error test method. Because prediction results of both rules have their own shortcoming, a new selection rules which uses Gray relational grade was proposed, and introduced to improved Gray Verhulst model in this paper. Genetic algorithm was used to select background function parameter ??, and Genetic algorithm parameters were selected by experiments. Gray relational grade was the fitness function in Genetic algorithm. Experiments and comparison with improved Gray Verhulst model demonstrate that the algorithm proposed in this paper has higher prediction accuracy than Gray model, and is feasible and dependable.