Low-density generator-matrix (LDGM) codes have advantages - fast encoding and parallel decoding, however the performance of the LDGM code is asymptotically bad. This problem can be solved by concatenating two LDGM codes serially. However, little is known about the construction of the concatenated LDGM codes - component LDGM codes, the combination of inner and outer coding rates, inner and outer code weights. In this paper, we investigate the parity check matrix of component LDGM codes that suited to concatenated LDGM codes. We also investigate appropriate combination of inner and outer coding rates and inner and outer code weights, and so on. In addition, we investigate how to set the maximum number of inner and outer iterations for concatenated LDGM codes. Our results are useful for the construction of concatenated LDGM codes.