To overcome the disadvantages of existing evaluation methods for scientific research project selection, a new evaluation approach based on the evidential reasoning algorithm under multi-dimensional frames of discernment is proposed. According to the logical relationship, the frames of discernment are distinguished to the parallel frame, progressive frame, and mixed frame. The comprehensive evaluation grade with the degree of familiarity and the funding advice plus the degree of familiarity in the peer review form are regarded as two parallel progressive frames and are transformed into pieces of evidence, where the peer reviews could be expressed by evaluation grades (funding advice) with belief. In this way, the incomplete information of peer reviews is able to be easily described and the valuable information of assessment could be fully integrated. Then the expert weights are given by the degree of familiarity and the peer reviews are integrated on two parallel frames, respectively by using the evidential reasoning operator. And then the evaluations of scientific research projects are quantified and selected. Finally, an example is given to check the validation of the approach.