Abstract: A generalized evidence theory, named as open frame Dempster-Shafer theory (OFDST), is proposed in the case of that a completed frame of discernment is unavailable. In the OFDST, the evidence's model is based on an open frame of discernment which will be complemented and enriched gradually during evidence combination. With the support function and objecting function defined on the OFDST, a novel interpretation of the evidence's belief function model is presented and the linear essence of the Dempster's rule of combination is demonstrated. Finally, an example is presented to illustrate the rationality and effectiveness of this theory.