The implementation of railway infrastructure construction projects including sustainable development goals is a complex process characterized by a significant extension of individual investment stages. The need for additional works has a big impact on construction railway projects, representing a risk which is the result of many different factors. During the execution of works, both the design assumptions and the conditions of the project’s implementation can be changed. An attempt to eliminate potential risks is a key element of construction projects. The article proposes a proprietary management method for the risk of additional works in railway projects. A methodology for creating risk management strategies using a standard algorithm that includes risk identification, risk analysis, and risk assessment is presented. The original elements of the work include risk identification followed by analysis using Bayesian networks. Using the example of a scenario of events, it is shown that a well-programmed network can be used to implement risk mitigation methods. Using the network, it is possible to compare different ways to reduce risk, check the effect of reducing the risk factors, and determine a satisfactory level of effects, e.g., increased financial resources as a result of additional works.