  In this article, we study the axial-vector tetraquark state and
two-quark-tetraquark mixed state consist of light quarks using the QCD sum
rules. The present predictions disfavor assigning the $a_1(1420)$ as the
axial-vector tetraquark state with $J^{PC}=1^{++}$, while support assigning the
$a_1(1420)$ as the axial-vector two-quark-tetraquark mixed state.
