<p>We, in this paper, focus on partially linear varying-coefficient quantile regression model when the response is subject to random left-truncation and the covariates are missing at random. Utilizing a weighted adjustment method, we propose a three-stage procedure to estimate both the unknown parametric and nonparametric components, establishing the asymptotic distributions of the resulting estimators. Further, restricted estimators of the linear regression coefficients and the corresponding test statistics are developed under both the null and local alternative hypotheses. To facilitate variable selection, we develop a penalization-based procedure and establish the oracle properties of the penalized estimators. As a by-product, we derive an asymptotic expression of the estimator targeting the distribution function of the left-truncated variable. Finally, simulation studies and real data analysis are conducted to evaluate the finite sample behaviors of the proposed methods.</p>