<p>In this article, we consider a new estimation method for partially linear additive quantile regression with missing covariates, which can accept many different missingness settings. This method approximates the nonlinear part based on B-spline, and incorporates multiply missing probability model assumptions into the construction of sample weights. Therefore, the multiply robust estimation method based on B-spline approximation is established for partially linear additive quantile model. To identify important variables in the linear part, we also study the variable selection problem by combining the nonconvex variable selection methods SCAD and MCP with the proposed multiply robust estimation method based on B-spline approximation. Under some regular conditions, the theoretical properties of multiply robust estimation and variable selection methods are studied. We provide the asymptotic normality of multiply robust estimation and the oracle property of variable selection methods. The performance of the proposed method is evaluated by using simulations. And the method is applied to the instance data of diuretic resistance.</p>