Abstract: The systematic generalized repeat-accumulate (GRA) code is constituted by a repeater, an interleaver, a combiner and a generalized accumulator. Under the belief propagation (BP) decoding of low density parity check (LDPC) codes, the performance of the GRA codes be affected by small cycles of the sparse parity check matrix which depends on encoding method. In this paper we present an optimized method for a class of GRA codes design. The parity check matrix is constructed based on the joint design between interleaver and combiner under the demand of no 4-cycles. With the simple encoding, simulation results show that the class of GRA codes outperforms conventional RA codes.