This paper presents a novel Bi-Intra Prediction (BIP) algorithm to improve intra coding performance for the next generation of video coding. In the proposed algorithm, a new predictor is generated by combining two existing intra prediction modes as an additional mode, being able to provide more accurate prediction. To remove the number of unnecessary combinations, restrictions on the search candidates and block sizes are carried out based on the statistical analyses. In addition, an efficient mode coding method of syntax elements in BIP is introduced to improve the coding performance. Moreover, a rough mode decision scheme is adopted to avoid high computation complexity in encoder side. Experimental results show that compared with the Versatile Video Coding reference software VTM-1.0, the proposed algorithm achieves 0.71%, 0.46% and 0.43% BD-Rate gains on average for Y, U and V components under all intra configuration, respectively, and 0.32%, 0.39%, 0.49% BD-Rate gains under random access configuration.