The fast decoding of low-density parity-check (LDPC) is crucial for its future applications. In this paper, we propose to use Early Termination (ET) and Force Convergence (FC) techniques to accelerate the decoding of two new local/global two-phases decoding algorithms to reduce the Globally Coupled (GC) LDPC codes. Specifically, ET is applied in the local decoding phase of two- phases decoding of GC-LDPC codes to skip the local decoding which is highly likely to fail and avoid the unnecessary iterations. FC is applied in global decoding phase where converged variable nodes are identified and removed from Tanner graph and the decoding can be speed up shrinking parity check matrices. Two variants are proposed for the ET operation in local decoding phase. ET-1 merely stops iteration if it meets the stopping criterion while in ET-1, the iteration number saved in local decoding is added up in global decoding to improve the decoding performance. The simulation results show that the ET-1-FC scheme can save up to 42% decoding time complexity in the low SNR region while keeping the error rate performance nearly unchanged, the ET-2-FC can improve the error rate performance by 0.18dB at bit error rate 0.001 or 0.23dB at frame error rate 0.1. In the waterfalling region of BER/FER curves, both schemes can save about 25% decoding time complexity.