In this article, quantile regression methods are suggested for a class of smooth coefficient time series models. We use both local polynomial and local constant fitting schemes to estimate the smooth coefficients in a quantile framework. We establish the asymptotic properties of both the local polynomial and local constant estimators for α-mixing time series. Also, a bandwidth selector based on the nonparametric version of the Akaike information criterion is suggested, together with a consistent estimate of the asymptotic covariance matrix. Furthermore, the asymptotic behaviors of the estimators at boundaries are examined. A comparison of the local polynomial quantile estimator with the local constant estimator is presented. A simulation study is carried out to illustrate the performance of estimates. An empirical application of the model to real data further demonstrates the potential of the proposed modeling procedures.