Time-delay reservoir computing uses a nonlinear node associated with a feedback loop to construct a large number of virtual neurons in the neural network. The clock cycle of the computing network is usually synchronous with the delay time of the feedback loop, which substantially constrains the flexibility of hardware implementations. This work shows an asynchronous reservoir computing network based on a semiconductor laser with an optical feedback loop, where the clock cycle (20 ns) is considerably different to the delay time (77 ns). The performance of this asynchronous network is experimentally investigated under various operation conditions. It is proved that the asynchronous reservoir computing shows highly competitive performance on the prediction task of Santa Fe chaotic time series, in comparison with the synchronous counterparts.