We develop a model of quantile treatment effects with endogeneity. The model exploits similarity assumption as a main identifying restriction. From this model we derive a Wald IV equation, and show that the model does not require functional form assumptions for identification. We characterize the quantile treatment function as solving an inverse quantile regression problem and suggest its finite-sample analog as a practical estimator. This estimator, unlike GMM, can be easily computed by solving a series of conventional quantile regressions, and does not require grid searches over many parameters. Empirical applications illustrate the approach.