Students majored in construction management in Hanoi University of Civil Engineering, Vietnam, must complete an integrated project for graduation. The two popular types of projects, including developing construction bids and delivering construction packages, involve making decisions to select the best construction methods to deliver construction processes on sites. Construction method selection is to make a complex decision that takes into account a variety of factors, including technical feasibility, cost, time, quality, the environment, the risk of each alternative, and the resources that are available, among others. Students are instructed to conduct the selection in two stages: (i) prerequisite assessment and (ii) alternative comparison. Only the alternatives passing the prerequisite assessment with all criteria related to technical requirements, quality, environmental aspects, and resources mobilization can be continued considering. The final stage uses a cost-equivalent measure to compare different alternatives with dissimilar costs and construction durations. In order to make an integrated sustainability-led decision on construction methods, potential carbon emission generated from each alternative must be considered. The amount of carbon will be converted to cost equivalent using carbon credit price and integrated to the cost and time factors of each alternative accordingly for final comparison. The proposed method was substantiated through a case study on piling works, where the optimal choice involved utilizing two sets of equipment. This option not only resulted in a lower equivalent cost but also achieved a reduction in CO2 emissions by 349 kg.