Spatially coupled low-density parity-check convolutional codes (SC-LDPC-CCs) are a class of capacity approaching LDPC codes with low message recovery latency when a sliding window decoding is used. Recently, an edge spreading (unwrapping) approach has been proposed to generate a class of array-based SC-LDPC-CCs by partitioning a spreading matrix into a number of components. Applying the spreading matrix E as the exponent matrix of a QC-LDPC code, the relationship of 4-cycles between E and the corresponding SC-LDPC-CCs is investigated in two cases, in this paper. Then, by defining a new class of integer finite sequences, called good sequences , a class of 4-cycle free SC-LDPC-CCs is constructed by an explicit simple method that can achieve (in most cases) the minimum coupling widths. The constructed codes enjoy a relative advantage in flexibility in rate and lengths, simple constructions, and minimal short-cycle distributions, which can show themselves in improving the bit-error-rate performances.