Given a network $G(N,\!A,\!C)$ and a directed path $P^0$ from the source node s to the sink node t, an inverse multi-objective shortest path problem is to modify the cost matrix C so that $P^0$ becomes an efficient path and the modification is minimized. In this paper, the modification is measured by the bottleneck type weighted Hamming distance and is proposed an algorithm to solve the inverse problem. Our proposed algorithm can be applied for some other inverse multiobjective problem. As an example, we will mention how the algorithm is used to solve the inverse multi-objective minimum spanning tree problem under the bottleneck type weighted Hamming distance.