Display omitted •The risk evaluation of construction project is described as a MCDM problem with the PFNs.•A PFNP model is proposed to overcome the limitations of the extant picture fuzzy projection model.•A picture fuzzy entropy weight method is introduced to obtain an objective weight vector of criteria.•PFNP-VIKOR method is developed to rank risk factors of construction project. Identifying the priority of risk factors through risk evaluation is a significant decision-making problem for construction project management team. In this study, a multi-criteria decision-making framework is constructed for risk evaluation of construction project with picture fuzzy information. First, several limitations of the extant picture fuzzy projection model are identified. Second, a picture fuzzy normalized projection (PFNP) model is proposed to overcome the limitations of the extant picture fuzzy projection model. Third, an entropy weight method of picture fuzzy sets is established to calculate the objective weight vector of the criteria. Furthermore, an integrated picture fuzzy normalized projection-based VIKOR method is constructed by integrate the PFNP model and VIKOR method under picture fuzzy environment. The proposed method not only considers the difference between two picture fuzzy numbers (PFNs), including distance and included angle, but also considers the compromise among the criteria. Finally, a case study, sensitivity analysis, and comparative analysis are conducted to interpret the practicality and validity of the proposed method.