Research and development (R&D) project risk assessment mainly focuses on predicting the likelihood of project success and effectively controlling risks. The belief rule-based (BRB) inference method has been applied for risk assessment, due to its strong interpretability and high prediction accuracy. However, lots of risk factors related to R&D projects will lead to an oversized rule base when the standard BRB method is used to evaluate project performance. In this research, a novel predictive evaluation framework is proposed to address this issue, where a RS-BRB model, namely the BRB with random subspaces, is developed to assess R&D project risks in a modular way. Firstly, multiple subspaces with low dimensions are constructed by random sampling. Subsequently, a BRB subsystem is developed as a base learner in each subspace to obtain a prediction result, and the evidential reasoning rule is adopted to combine the prediction results from different BRB subsystems. The proposed model was validated using the data from R&D projects in Chinese industries. Comparative analysis results show that the proposed model has superior prediction accuracy and can overcome the problem of combinational explosions without information loss.