Abstract: 〖JP2〗A new algebraic construction of regular, time-invariant low-density parity-check (LDPC) convolutional codes with fast encoding based on finite fields is proposed in this paper. 〖JP2〗It is first specified the structure properties of a base matrix which is associated with a〖JP〗 quasi-cyclic (QC) LDPC code constructed based on finite fields GF(q). A concrete algebraic construction and its modified form of the matrix are then given. Finally, according to the ring isomorphism relationship between a QC code and a convolutional LDPC code, the polynomial 〖JP〗matrix corresponding to an LDPC convolutional code with fast encoding is developed. The algebraic construction simplifies the construction process significantly. In particular, the fast encoding property can both reduce the encoding complexity and simplify encoder structure. Simulation results show that the proposed LDPC convolutional codes have more excellent performance in comparison with the existing counterparts under belief propagation (BP) decoding algorithm over additive Gaussian white noise (AWGN) channels.