When analyzing the relative performance of mutual funds, current data envelopment analysis (DEA) models with diversification only consider risks and returns over the entire investment process, which ignore the performance change in consecutive periods. This paper introduces a novel multi-period network DEA approach with diversification and the directional distance function. The new approach decomposes the overall efficiency of a mutual fund in the whole investment interval into efficiencies at individual periods. At each period, mutual funds consume exogenous inputs and intermediate products produced from the preceding period to produce exogenous outputs and intermediate products for the next period to use. Efficiency decomposition reveals the time at which the inefficiency happens. The new model can provide expected inputs, outputs and intermediate variables at individual periods, which are helpful for fund managers to take effective ways to improve the fund performance. Under the assumption of discrete return distributions and a proper choice of inputs, outputs and intermediate variables, the proposed models can be transformed into linear programs. The applicability and reasonability of the proposed method are demonstrated by applying it to assess the relative performance of 40 open-ended funds in Chinese security markets.