A method of constructing low-density parity-check (LDPC) codes is presented, where an identity matrix is combined with another sub-matrix constructed under the condition of a given girth and fixed weight of column to generate a parity check matrix. Let Wc denote the fixed weight of column, which is usually not
less than 3. Two kinds of check matrices sized 28×76 and 64×328 are constructed. Simulation results over additive white Gaussian noise (AWGN) channels show that performance of the codes is better than that of check matrices sized 42×105, 170×425 and 66×330. Meanwhile, sufficient conditions for the girth of Tanner graph based on Matroid theory are present. The girth conditions can be used to construct LDPC codes with given short girths. High-rate LDPC codes with short block length can be applied to the future digital video broadcast-handsets.