Design–build (DB) projects have become increasingly popular for construction projects in developing countries due to the cost and scheduling advantages and their design optimization ability. As a result, much research has been conducted on improving DB efficiency in terms of cost, scheduling, risk management, etc. However, the existing studies have mainly focused on the owner’s roles, whereas general contractors (GCs) must also take many risks on behalf of owners in DB projects. The adequate identification and assessment of risks before engaging a contractor can increase the likelihood of a project’s success, at least from a DB contractor’s perspective. Therefore, this study interviewed procurement experts to conduct a survey at the local level, then analyzed, developed, and proposed an additional risk management process (RMP) for use by GCs during the bidding process of DB projects. A case study was conducted with a large Vietnamese GC to evaluate the effectiveness of the process and find ways to optimize it in the future. The results of the study showed that risk management during a DB project is imperative. Nevertheless, preparing bids is time-consuming and increases the contingency costs, reducing the competitiveness of the bid prices for contractors. Therefore, depending on the specific project and risk management objectives, an RMP is recommended for adjusting the risk management target to reduce the risk, while still maintaining the competitiveness of the bid prices.