In this paper, we propose a multivariate random forest method for multiple responses of mixed types with missing responses. Imputation is performed for each bootstrap sample used to build the individual trees that form the forest. The individual trees are built using a weighted splitting rule allowing down-weighting of imputed observations. A simulation study shows the benefits of this approach over complete case analysis when missing responses are MCAR and MAR. In particular, the gain in prediction accuracy of the proposed method is larger in the MAR case and also increases as the proportion of missing increases.