In this paper, we study a shore power deployment problem in a container shipping network. The aim of the problem is to develop a subsidy program for a government that achieves the utmost reduction of at-berth emissions from ships in the network. We formulate the problem as a mathematical model that captures the involved relationships among the government, container ports, and shipping lines. The model is hard to solve because it involves a multi-phase process that does not have a closed-form solution. To solve the problem, we develop a tailored labeling algorithm. Extensive numerical experiments are conducted, and the results demonstrate the applicability and efficiency of the solution method for solving practical instances. The results also demonstrate that the solutions delivered by our algorithm to the problem can significantly reduce the at-berth emissions from ships in the shipping network.