Rail traortation network design, concentrating on establishing new rail corridors, developing existing corridors’ capacities, and interaction between rail corridors and logistics centers, is one of the substantial and strategic issues in the field of traortation. Finding an optimal solution to this problem, considering capacity constraints and network pricing, can lead the freight traortation demand to the green rail mode and reduce economic, environmental, and social costs. In this paper, for the first time, a three-level integrated intermodal network design problem (MIINDP) with consideration of modal competition, network elements’ capacity constraints, budget limitation, and different actors’ points of view is addressed. On upper-level, intermodal terminal and rail corridor candidates are selected by concentrating on budget limitation. On the middle level, road and rail and intermodal annual freight demand are calculated by logit discrete choice model, and freight demand will be updated. Finally, the demands are assigned to lower-cost routes capacity-based incremental assignment method. In this problem, freight demand is assigned to the networks based on four types of rail accessibility of origins and destinations. Due to capacity constraints in rail traortation system, it is possible to exist unmet rail/intermodal annual fright demand of an OD-pair. Therefore, in this situation, the demand is assigned to OD-pair’s lowest-cost road route. A mathematical programming model is formulated, aimed to minimize the total cost, including both internal and external costs of freight traortation in rail and road networks. In the proposed mathematical model, the government selects candidates due to budget limitation to minimize the network’s total cost after applying the logit model and choosing the appropriate traortation mode by the freights’ owners. It is worth noting that the b freight’s owners choose the reasonable traortation mode without considering the external costs and only by regarding internalities. Although, the government considers the total cost of the network after allocating all the freight demand, by imposing externalities. Due to the NP-hardness of the problem, an innovative solution approach, based on genetic algorithm and heuristic indices are proposed and implemented in the Java programming environment. The heuristic indices and the Roulette wheel heuristic algorithm are employed to restrict the candidate combinations and to initialize a genetic algorithm population. To prioritize establishment and development candidates, candidate’s Absolute Priority Index (API) is introduced to designate the importance of each candidate for choosing. Besides, another heuristic index, named Similarity Index (SI) is defined to determine the similarity of candidates. Also, to evaluate and validate the proposed solution approach, some examples are designed in small-scale and compared with each other. This comparison indicates that the results obtained from the proposed solution approach differ by a maximum of 0.085% from the optimal solution, obtained from the exact exhaustive enumeration algorithm. However, the average solution times of the designed examples by the exhaustive enumeration algorithm and the proposed solution approach are 3600 and 240 minutes, respectively. Then, with consideration of establishing and developing rail corridor candidates in Iran’s rail traortation network, and also different amounts of budget, optimal integrated Iran’s rail network design was presented. Some examples of Iran Rail Network by considering the origin-destination demand matrix of different good groups in the year 1414 (including 390 centroids) And 247 candidates (45 intermodal terminals and 202 rail corridors) were solved. The average time to solve each of the problems using the proposed solution approach in the research was 1500 minutes. As a consequence of this paper, considering a higher budget and establishing more candidates does not necessarily lead to lower external costs of rail and road networks. This managerial insight means that there may be scenarios of rail network design, in which, the external costs are less than the external costs in the complete network (existing all candidates).The achievementof this paper can be used as an effective and efficient tool for policy making and prioritization of railway network infrastructure projects. Keywords: Environmentally friendly modes, Multilevel integrated intermodal network design problem, External costs, Rail accessibility, Heuristic indices.