H. Wang considered the minimum degrees condition that $G$ has large vertex-disjoint cycles in bipartite graphs. Motivated by this, we consider the small vertex-disjoint cycles in bipartite graphs in this paper. We prove the following result: Let $m\ge 3$, $n\ge 2$ and $k\ge 1$ be three integers. Let $G=(V_1,V_2;E)$ be a bipartite graph with $|V_1|=|V_2|=n\ge 2k+1$. If the minimum degree $\delta (G)\ge k+1$ and $\sum _{x\in V(C)}d(x)\ge m(n+1)+1$ for any cycle $C$ of $G$ with length $2m$, then $G$ contains $k$ vertex-disjoint cycles of length 4. Moreover, the degrees condition is sharp.