Stochastic dynamic investment games with regime switching model in continuous time between two investors are developed. The market coefficients are modulated by continuous-time Markov chain. There is a single payoff function which depends on both investors? wealth processes. One player chooses a dynamic portfolio strategy in order to maximize this expected payoff, while his opponent is simultaneously choosing a dynamic portfolio strategy so as to minimize the same quantity. A general result in optimal control for a stochastic differential game with a general payoff function is presented under some regular conditions. Use this general result to utility-based games of fixed duration, the optimal strategies and value of the games are derived explicitly.