We study quantile regression (QR) for longitudinal measurements with nonignorable intermittent missing data and dropout. Compared to conventional mean regression, quantile regression can characterize the entire conditional distribution of the outcome variable, and is more robust to outliers and misspecification of the error distribution. We account for the within-subject correlation by introducing a l(2) penalty in the usual QR check function to shrink the subject-specific intercepts and slopes toward the common population values. The informative missing data are assumed to be related to the longitudinal outcome process through the shared latent random effects. We assess the performance of the proposed method using simulation studies, and illustrate it with data from a pediatric AIDS clinical trial.