Finite mixture regression (FMR) is widely used for modeling data that originate from heterogeneous populations. In these settings, FMR can offer increased predictive power compared to more traditional one-class models. However, existing FMR methods rely heavily on mixtures of linear models, where the linear predictor must be given as an input. A flexible FMR model is presented using a combination of the random forest learner and a penalized linear FMR. The performance of the new method is assessed by predictive log-likelihood in extensive simulation studies. The method is shown to achieve equal performance with the existing FMR methods when the true regression functions are in fact linear and superior performance in cases where at least one of the regression functions is nonlinear. The method can handle a large number of covariates, and its predictive ability is not greatly affected by surplus variables.