In the fast-moving and competitive market conditions, port operators need to improve their competitiveness to attract more customers. With the rise of stakeholders' (e.g., shippers and port operators) environmental concerns, intermodal transport offers an opportunity to reduce environmental impacts and improves port competitiveness, due to the benefit on environmental protection. However, it is a challenge to understand how port operators make their plans for intermodal network design with consideration for port competition, shippers' route choice behaviors and environmental concerns of stakeholders. In this paper, we develop a game-theoretical model of port competition with environmental concerns. A logit model is used to formulate shippers' discrete choice behaviors. With respect to the probability of nonexistence of pure Nash equilibrium, we propose an approximate equilibrium and a corresponding solution algorithm. A case study on the competition between Dalian port and Yingkou port in the northeast of China is used to verify the effectiveness of the proposed model and algorithm. Results show that, in competitive settings, the rise of stakeholders' environmental concerns will make the market less competitive and always be beneficial to the port closer to the market (here Yingkou port). Moreover, when shippers pay more attention to the environment, the total CO₂e emissions will decrease. As the number of dry ports increases, the CO₂e emissions will decrease. There are also some interesting findings of effects of environmental concerns on the intermodal network, profits, and CO₂e emissions.