Orthogonal frequency division multiplexing (OFDM) usually suffers high peak-to-average power ratio (PAPR). As shown in this paper, PAPR becomes even severe for sparse source due to many identical nonzero frequency OFDM symbols. Thus, this paper introduces compressive coded modulation (CCM) in order to restrain PAPR by reducing identical nonzero frequency symbols for sparse source. As a result, the proposed CCM-based OFDM system, together with iterative clipping and filtering, can efficiently restrain the high PAPR for sparse source. Simulation results show that it outperforms about 4 dB over the traditional OFDM system when source sparsity is 0.1.