A girth ACE union (GAU) construction algorithm is proposed for variably long LDPC codes considering the degree distribution, girth and approximate cycle extrinsic (ACE) message degree in a unified architecture. Therefore the short cycle number is reduced and the extrinsic message degree is increased. Large range of variable code length is accommodated through parity check matrix constructed by GAU algorithm. For short length codes, the performance of GAU algorithm is similar with that of LDPC codes in IEEE 802.16e. For middle length and long codes, GAU algorithm performs a little better. Variably long LDPC codes are designed using a common parity check matrix. The design of encoder and decoder with the same architecture for variable lengths is facilitated, which reduce the realizing complexity of encoder and decoder. Results show that the algorithm is useful in designing LDPC codes, which support variably long data communication, and the research is meaningful both in theory and practice.