In order to analyze the complex constitutive behavior of titanium alloy under different strain rates, a new titanium alloy viscoplastic constitutive model is proposed basing on the plastic deformation mechanism and the dislocation dynamics theory. The relationship of model parameters and micro structure characteristics, as well as the physical significance are described. As the constitutive model contains 12 undetermined parameters, the identification of parameters would be computationally expensive. An overall analysis method of parameter sensitivity based on the Latin Hypercube Sampling (LHS) method and spearman rank correlation method is developed, which is effective and accurate enough in identifying parameters. Furthermore, on the fundamental of the analytic result of parameter sensitivity and basic Genetic Algorithm (GA), an advanced genetic algorithm based on the advanced niche genetic algorithm, global peak value determination strategy and local accurate searching techniques is developed. Finally, taking Ti-6Al-4V alloy as example, the single axis flow stress-plastic strain curve of this alloy under different strain rates and temperatures is described, and the results of numeric simulation matches very well with experiment data from the existed reference.