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We have presented a detailed study of twist-2 and twist-3 light-cone distribution amplitudes of
1
P
1
3
and
1
P
1
1
axial-vector mesons, based on QCD conformal partial wave expansion. Applying equations of motion, the twist-three two-parton light-cone distribution amplitudes can be expressed in terms of leading-twist and twist-three three-parton light-cone distribution amplitudes. The relevant G-parity invariant and violating parameters, containing the corrections due to the
SU
(
3
)
breaking effects, are evaluated from the QCD sum rule method. The results for axial-vector decay constants of
1
P
1
3
states are presented. The values of tensor decay constants and Gegenbauer moments of the leading twist distribution amplitudes for
1
P
1
1
states are updated. Using Gell-Mann–Okubo mass formula, the mixing angle for the
f
8
and
f
1
of
1
P
1
3
states is
θ
P
1
3
∼
38
°
, and that for
h
8
and
h
1
of
1
P
1
1
states is
θ
P
1
1
∼
10
°
. The detailed properties for physical states
f
1
(
1285
)
,
f
1
(
1420
)
,
h
1
(
1170
)
, and
h
1
(
1380
)
are given. Assuming the mixing angle between
K
1
A
and
K
1
B
to be
θ
K
=
45
°
or −45°, we also give the detailed study for
K
1
(
1270
)
and
K
1
(
1400
)
. Using the conformal partial wave expansion, we obtain the models for light-cone distribution amplitudes, containing contributions up to conformal spin 9/2. It is interesting to note that some distribution amplitudes have significant asymmetric behaviors, which should be phenomenologically attractive.