For the speckle noise in laser display, a speckle reduction method by the spectral broadening is proposed, which is based on the external cavity semiconductor laser system. Firstly, by appropriately tuning the feedback ratio, the state of coherence collapse is obtained using the optical-feedback-induced self-mixing interference and can be harnessed for the realization of the spectrally broadband emission. Then the optimized broadband laser source is utilized in the speckle measurement system. Significant speckle reduction can be achieved by the spectral broadening due to the low temporal coherence properties of lights. Experimental results show the performance of the proposed approach. The extraordinarily high spectral bandwidth of about 6 nm with multimode emission is achieved in the coherence collapsed state. In free-space reflection geometry, the speckle contrast has been successfully reduced down to 0.049 with this broadband laser source.