LDPC block codes (LDPC-BCs) have attracted great interests in recent years by highly parallel computation and good bit-error-rate performance, and one of the decoder implementation issues is high routing complexity. LDPC convolutional codes (LDPC-CCs) not only release routing complexity but also are natural to dynamic length of data frame. Thus, the codes are very suitable for video stream and pre-5G wireless communication systems. LDPC-CC decoder is composed of several concatenated processors, where the long FIFOs are usually the bottleneck of area and decoding latency. To improve hardware efficiency, we use overlapped architecture to share partial FIFO between processors. Furthermore, check node unit and hybrid-partitioned FIFO are proposed to increase throughput and pipeline efficiency. The measurement results of test chip in 65nm technology show that our work can achieves 7.72 Gb/s under 322MHz operating frequency. The decoder with 6 processors occupies an area of 1.19 mm2, drawing 410.5 mW of power with an energy efficiency of 8.75pJ/bit/proc.