Two families A ⊆ [ n ] k and B ⊆ [ n ] ℓ are called cross- t -intersecting if | A ∩ B | ≥ t for all A ∈ A , B ∈ B . Let n , k and ℓ be positive integers such that n ≥ 3 . 38 ℓ and ℓ ≥ k ≥ 2 . In this paper, we will determine the upper bound of | A | | B | for cross-2-intersecting families A ⊆ [ n ] k and B ⊆ [ n ] ℓ . The structures of the extremal families attaining the upper bound are also characterized. The similar result obtained by Tokushige can be considered as a special case of ours when k = ℓ , but under a more strong condition n > 3 . 42 k . Moreover, combined with the results obtained in this paper, the complicated extremal structures attaining the upper bound for nontrivial cases can be relatively easy to reach with similar techniques.