Reconciliation is an important step to correct errors in Quantum Key Distribution (QKD). In QKD, after comparing basis, two legitimate parties possess two correlative keys which have some differences and they could obtain identical keys through reconciliation. In this paper, we present a new rate compatible reconciliation scheme based on Row Combining with Edge Variation (RCEV) Low Density Parity Check (LDPC) codes which could change code rate adaptively in noisy channel where error rate may change with time. Our scheme is easy to implement and could get good efficiency compared to existing schemes. Meanwhile, due to the inherent structure we use, the new scheme not only saves memory space remarkably but also simplifies the decoder architecture and accelerates the decoding.