In this paper we propose a hybrid approach using mutual information and multi-objective optimization for feature subset selection problem. The hybrid aspect is due to the sequence of a filter method and a wrapper method in order to take advantages of both. The filter method reduces the exploration space by keeping subsets having good internal properties and the wrapper method chooses among the remaining subsets with a classification performances criterion. In the filter step, the subsets are evaluated in a multi-objective way to ensure diversity within the subsets. The evaluation is based on the mutual information to estimate the dependency between features and classes and the redundancy between features within the same subset. We kept the non-dominated (Pareto optimal) subsets for the second step. In the wrapper step, the selection is made according to the stability of the subsets regarding classification performances during learning stage on a set of classifiers to avoid the specialization of the selected subsets for a given classifiers. The proposed hybrid approach is experimented on a variety of reference data sets and compared to the classical feature selection methods FSDD and mRMR. The resulting algorithm outperforms these algorithms and the computation complexity remains acceptable even if it increases with regards to these two fast selection methods.