A group divisible design GDD(v = v 1 + v 2 + · · · + v g,g, k, λ 1, λ 2) is an ordered triple (V, G, B), where V is a vset of symbols, G is a partition of V into g sets of size v 1, v 2,⋯ v g, each set being called group, and B is a collection of ksubsets (called blocks) ofV, such that each pair of symbols from the same group occurs in exactly λ 1 blocks; and each pair of symbols from different groups occurs in exactly λ 2 blocks. Here, we focus on an existence problem of GDDs with two associate classes or when g = 2, and with blocks of size 3, when the required designs have two groups of unequal sizes and λ 2 = 4. We obtain the necessary conditions and prove that these conditions are sufficient.