Based on the predictions of the relevant form factors from the covariant light-front quark model, we show the branching fractions for the D(D s ) → (P, S, V, A) ℓν ℓ (ℓ = e or µ) decays, where P denotes the pseudoscalar meson, S the scalar meson with a mass above 1 GeV, V the vector meson and A the axial-vector one. Comparison with the available experimental results are made, and we find an excellent agreement. The predictions for other decay modes can be tested in a charm factory, e.g., the BESIII detector. The future measurements will definitely further enrich our knowledge on the hadronic transition form factors as well as the inner structure of the even-parity mesons (S and A).