Interference alignment (IA) in uplink coordinated multipoint (CoMP) has been proved to be able to improve the performance in next generation mobile cellular systems. In this paper, an efficient codebook-based Max-SINR IA aided uplink (UL) CoMP scheme with full cooperation at the receiver is proposed. Compared to conventional IA, codebook-based IA requires less feedback information and maintains the same significant improvement in system capacity. To avoid the exhaustive precoder search in codebook-based IA, the K-Best selection algorithm is adopted to efficiently perform precoder selection. Simulation results demonstrate that the proposed codebook-based IA and K-Best precoder selection algorithm can achieve a significant performance gain especially in severe interference environments.