Applying Zvonkin's transform, the exponential convergence in Wasserstein distance for a class of functional SDEs with Dini continuous drift is obtained. This and the log-Harnack inequality implies the same convergence in the sense of entropy, which also yields the convergence in total variation norm by Pinsker's inequality. Moreover, the assertions above also hold for degenerate functional SDEs with H\"{o}lder continuous drift.