This paper is devoted to studying Bergman spaces Apω1,2 (M) (1 < p < ∞) induced by regular-weight ω1,2 on annulus M. We characterize the function f in L1ω1,2 (M) for which the induced Hankel operator Hf is bounded (or compact) from Apω1,2 (M) to Lqω1,2 (M) with 1 < p,q < ∞.