We construct a Heston‐type stochastic volatility model with a Markov switching regime to price a plain‐vanilla stock option. A semi‐analytic solution, which contains a matrix ODE is obtained and numerically calculated. Our model is flexible enough to provide a wide variety of volatility surfaces for the same volatility level but different regimes. © 2015 Wiley Periodicals, Inc. Jrl Fut Mark 36:902–919, 2016