The multi-objective evolutionary algorithm (MOEA) has shown remarkable capability of selecting feature subset. Most MOEAs use the cardinality of the feature subset as one of its objectives and adopt a strict Pareto dominance relationship to select individuals. However, these techniques limit available solutions and may omit several appropriate but dominated solutions. A multi-objective unsupervised feature selection algorithm (MOUFSA) is proposed to solve these issues. A new objective, which incorporates the correlation coefficient and cardinality of the feature subset, not only evaluates the redundancy of selected features but also provides several objective values for each particular size of feature subset. A relaxed archiving strategy based on negative epsilon-dominance and the box-based method is designed to preserve promising solutions even if they are dominate. Three new mutation operators of different abilities are also presented to enhance the algorithm. Nine UCI datasets and five fault recognition datasets are employed as test objects, and the obtained feature subsets are then used for subsequent classification and clustering. Experimental results show that MOUFSA outperforms several other multi-objective and traditional single-objective methods.