Summary: We investigate a functional additive quantile regression that models the conditional quantile of a scalar response based on the nonparametric effects of a functional predictor. We model the nonparametric effects of the principal component scores as additive components, which are approximated by B-splines. We select the relevant components using a nonconvex smoothly clipped absolute deviation (SCAD) penalty. We establish that, when the relevant components are known, the convergence rate of the estimator using the estimated principal component scores is the same as that using the true scores. We also show that the estimator based on relevant components is a local solution of the SCAD penalized quantile regression problem. The practical performance of the proposed method is illustrated using simulation studies and an empirical application to corn yield data.