In this paper, we study the linear quantile regression model when response data are missing at random. Based on the inverse probability weight method, we establish an estimation equation on quantile regression and define standard quantile regression estimator of unknown parameter. At the same time, we construct the empirical likelihood (EL) ratio function for the unknown parameter, and define the maximum EL estimator of the unknown parameter. Under suitable assumptions, we investigate the asymptotic normality of the proposed estimators and prove the EL ratio statistics has a standard chi-squared limiting distribution. A simulation study is done to investigate the finite sample performance of the estimators and compare the difference of the proposed EL method and bootstrap approach.