A non-symmetrical Bouc-Wen model is proposed in this paper for magnetorheological (MR) fluid dampers. The model considers the effect of non-symmetrical hysteresis which has not been taken into account in the original Bouc-Wen model. The model parameters are identified with a Genetic Algorithm (GA) using its flexibility in identification of complex dynamics. The computational efficiency of the proposed GA is improved with the absorption of the selection stage into the crossover and mutation operations. Crossover and mutation are also made adaptive to the fitness values such that their probabilities need not be user-specified. Instead of using a sufficiently number of generations or a pre-determined fitness value, the algorithm termination criterion is formulated on the basis of a statistical hypothesis test, thus enhancing the performance of the parameter identification. Experimental test data of the damper displacement and force are used to verify the proposed approach with satisfactory parameter identification results.