In an edge-labeling of a graph \(G\), the vertex sum at a vertex \(v\) is defined as the sum of labels of the edges incident to \(v\). A graph \(G\) is antimagic if there exists a bijective edge labeling from \(E(G)\) to \(\{1,2,\dots,|E(G)|\}\) such that the vertex sums are pairwise distinct. In this paper, the authors prove that the connected \((2,k)\)-biregular \((k\geq 3)\) bipartite graph, \((k,pk)\)-biregular \((k\geq 3,p\geq 2)\) bipartite graph and \((k,k^2+y)\)-biregular \((k\geq 3,y\geq 1)\) bipartite graph are antimagic. Also, they discuss the antimagic labeling of disconnected \((2,k)\)-biregular \((k\geq 3)\) bipartite graphs.