With the emergence of numerical sensors in many aspects of everyday life, there is an increasing need in analyzing multivariate functional data. This work fo-cuses on the clustering of those functional data, in order to ease their modeling and understanding. To this end, a novel clustering technique for multivariate functional data is presented. This method is based on a functional latent mixture model which fits the data in group-specific functional subspaces through a multivariate functional principal component analysis. A family of parsimonious models is obtained by constraining model parameters within and between groups. An EM-like algorithm is proposed for model inference and the choice of hyper-parameters is addressed through model selection. Numerical experiments on simulated datasets highlight the good performance of the proposed methodology compared to existing work. This algorithm is then applied for analyzing the pollution in U.S. cities for one year.