Optical chaos communication encounters difficulty in high-speed transmission due to the challenge of realizing wideband chaos synchronization. Here, we experimentally demonstrate a wideband chaos synchronization using discrete-mode semiconductor lasers (DMLs) in a master-slave open-loop configuration. The DML can generate wideband chaos with a 10-dB bandwidth of 30 GHz under simple external mirror feedback. By injecting the wideband chaos into a slave DML, an injection-locking chaos synchronization with synchronization coefficient of 0.888 is realized. A parameter range with frequency detuning of -18.75 GHz to approximately 1.25 GHz under strong injection is identified for yielding the wideband synchronization. In addition, we find it more susceptible to achieve the wideband synchronization using the slave DML with lower bias current and smaller relaxation oscillation frequency.