Code block group (CBG) based hybrid automatic repeat request (HARQ) has the advantage of low feedback overhead, but the drawback is the relatively poor transmission efficiency. This letter aims to improve the transmission efficiency of CBG-based HARQ. Based on the fact that, during the retransmission phase, the receiver already has the a prior information of the erroneous codewords, we propose a new scheme to exploit the redundancy. Specifically, all codewords corresponding to the erroneous CBG are linearly compressed into multiple compressed codewords which are transmitted over the channel instead of all corresponding ones. Simulation results show that the proposed compressed CBG-HARQ can achieve a significant higher throughput than the existing group-based HARQ schemes with only one bit feedback overhead at the cost of a marginal increase in complexity.