In this paper, we investigate Tanner's lower bound for the minimum distance of regular LDPC codes based on combinatorial designs. We first determine Tanner's lower bound for LDPC codes which are defined by modifying bipartite graphs obtained from combinatorial designs known as Steiner systems. Then we show that Tanner's lower bound agrees with or exceeds conventional lower bounds including the BCH bound, and gives the true minimum distance for some EG-LDPC codes.