This article establishes a hybrid model by adding into the Heston-Vasicek model an additional regime switching factor, which combines the advantages of the stochastic interest rate, regime switching, and multi-factor stochastic volatility. It assumes a Vasicek stochastic interest rate, and uses two stochastic factors for asset volatility, one of which follows Heston stochastic volatility and another can switch according to a continuous-time Markov chain. Such a setting considers both effects of economic cycles and the correlation between the stock and interest rate, while still ensuring the existence of an analytical solution for European option pricing. We further showed how option prices evolve when varying certain model parameters. An empirical study was also carried out to demonstrate the model performance if it was to be applied in practice.