<p>This paper is concerned with quantile regression estimation and variable selection for partially linear varying coefficient models with nonignorable missing responses. To address the identifiability issue, we use a nonresponse instrument and estimate the propensity based on the generalized method of moments. Once the propensity is estimated, we construct bias-corrected quantile regression estimators for both the parametric regression coefficients and the varying coefficient functions utilizing inverse propensity weighting and B-spline approximation approaches. The asymptotic properties of the resulting estimators are established. We further consider the penalized estimator of the parameter part and derive its oracle property. The finite sample performance of the proposed method is evaluated through simulation studies, and its value is illustrated by an application to the HIV-CD4 data.</p>