The completion of a bridge construction project within budget is one of the project’s key factors of success. This prerequisite is more likely to be achieved if the cost estimates, especially those provided in the early stage of a project, are realistic and close to the actual costs. The paper presents the research results on the development of a cost prediction model based on machine learning, namely the support vector machines (SVM) method, for which the input represents basic information and parameters of bridges, available in the early stage of projects. Several SVM-based regression models were investigated with the use of data collected for a number of bridge construction projects completed in Poland. Having finished the machine learning and testing processes, five of the models, of satisfying knowledge generalization ability and comparable performance, were preselected. The final selection of the best model was based on the comparison and analysis ability to predict bridge construction costs with accuracy appropriate for the early stage of projects. The general testing metrics of the finally selected model, named BCCPMSVR2, were as follows: root mean square error: 1.111; correlation coefficient of real-life bridge construction costs and costs predicted by the model: 0.980; and mean absolute percentage error: 10.94%. The research resulted in the development and introduction of an original model capable of providing early estimates of bridge construction costs with satisfactory accuracy.