Enhanced indexation model( EIM) adopts some of the constituents to construct a portfolio to track the benchmark index and obtain excess returns. As the benchmark index falls,the tracking portfolio follows and yield negative returns. Therefore,it is necessary to add downside risk constraints to the traditional EIM in order to prevent the tracking portfolio from jumping in conjunction with severe market recession. It is noticeable that,as a downside risk measure,the lower partial moment( LPM) has good theoretical properties and covers the classical measures such as loss probability,expected loss,and lower semi-variance. In this paper,an EIM with the LPM constraint is constructed. Its key characteristics are threefolds. First,our model has a more general objective function to meet investors' risk preferences. By adjusting the balanced parameter,our model can be degenerated to the traditional index replication model and excess returns maximum model. Second,the nonparametric LPM constraint is added to our model in order to control the downside risk of the tracking portfolio. Third,the objective function and the nonparametric first-order LPM are proven to be a convex function of the portfolio's position,and the EIM with nonparametric first-order LPM are proven to be a convex optimization problem. Finally,Monte Carlo simulation and the empirical results show that our model can effectively control the downside risk and obtain excess returns.