When carrying out the gene level association analysis based on functional linear model, it's required to numerically approximate the values of genetic variants in each genes. In order to improve the accuracy of approximations and reduce the time-consuming problem by using the traditional spline function in deducing functional linear model, this paper proposes a functional linear model based on Legendre polynomials, which can enhance the accuracy and efficiency of approximations in getting functional linear model due to the orthogonality. By analyzing the simulated genetic data, it knows that the proposed method can keep the reasonable type 1 error, enhance the statistical power, and reduce the computational time. Therefore, the functional linear model with Legendre polynomials has more practical application values than the traditional functional linear model in gene level association analysis.