In this work, we study the radiative leptonic decays of [Formula: see text] and [Formula: see text] mesons in the Standard Model (SM) and two-Higgs-doublet-model (2HDM) Type II. The results are obtained using the factorization procedure, and the contribution of the order [Formula: see text] is included. The numerical results are calculated using the wave function obtained in relativistic potential model. As a result, the decay mode [Formula: see text] is found to be sensitive to the effect of the charged Higgs boson. Using the constraint on the free parameters of 2HDM given in previous works, we find the contribution of the charged Higgs boson in the decay mode [Formula: see text] can be as large as about 13%.