Index tracking is an passive strategy in portfolio management, it mimics the performance of a benchmark index to construct portfolios for obtaining the average return of the target market. Index tracking has become popular in investors because it possesses the advantages of low cost, high liquidity and lower risk. This paper introduced sensitivity analysis to construct a fuzzy multi-objective index tracking portfolio model with value at risk (SA-IT-VAR-FMOPM) when return rate was set as parabolic fuzzy variable, the sensitivity and VaR factors were considered in the model. An improved particle swarm optimization (IPSO) algorithm was used to search optimal solution for multi-objective problem. To verify the effective of the proposed model, Dow 30 index data were selected to the empirical experiment, the results show the fuzzy multi-objective index tracking portfolio model which considered the sensitivity and VaR factors can obtain more stable portfolio and achieve the average return of target market. © 2018 IEEE.