We propose an intermodal hub location problem with market selection. The problem has a given number of markets and the revenue associated with each market. Each market has a predetermined demand, and the selected market demand has to be shipped from the origin to the destination via a hub-and-spoke system. The overall objective is to maximize the overall margins that are equal to the total revenue of the selected markets minus the total costs including the operating costs of intermodal hubs, transportation costs, and outsourcing costs. We propose a mixed integer programming model to formulate the problem without capacity constraints (IHL-MU). For the problem, we propose a Lagrangian relaxation based polynomial time algorithm that exploits the rich structure of the Lagrangian subproblems to obtain the objective values of the problems and their objective bounds efficiently. Specifically, we develop a polynomial time algorithm to solve the Lagrangian subproblems. The proposed method can obtain near-optimal solutions for large test instances, while the commercial software package (CPLEX 12.6) cannot achieve feasible solutions.