In this paper, we consider a network optimization interdiction problem, called the b-matching interdiction problem on bipartite graphs with unit weight and multi-dimensional budgets. Given an undirected bipartite graph G, every edge of G has a multi-dimensional interdiction costs and budget. The goal is to remove a subset of the edges constrained to a multi-dimensional budget, such that the maximum b-matching in the resulting graph is minimized. Let d be the dimension of the leader’s budget. We first show that b-matching interdiction problem is W[1]-hard with respect to the budget for the number of interdicted edges when \(d=2\) and graph contain only isolated edges. Then, we propose a \((d+1)\) -approximation algorithm on bipartite graphs via the iterative rounding method. Finally, we also show that our iterative rounding method is a 2-approximation algorithm when d is a constant.