In this work, the transition form factors are calculated for the semileptonic D (s) → Aℓ + ν where A = a1, b1, K1(1270, 1400), i.e., D + → a 0 1 (b 0 1 , K 0 1 )ℓ + ν, D 0 → a − 1 (b − 1 )ℓ + ν, and D + s → K 0 1 ℓ + ν in the frame work of the light-cone QCD sum rules (LCSR) approach up to the twist-3 distribution amplitudes (DAs). Since the masses of these axial vector mesons are comparable to the charm quark mass, we keep out in our calculations all terms including mA/mc in expansion of two-parton DAs. Branching ratio values are estimated for the semileptonic D (s) → Aℓν and nonleptonic D → K1(1270, 1400)π decays. A comparison is also made between our results and predictions of other methods and the existing experimental values.