Chaos, occurring in a deterministic system, has permeated various fields such as mathematics, physics, and life science. Consequently, the prediction of chaotic time series has received widespread attention and made significant progress. However, many problems, such as high computational complexity and difficulty in hardware implementation, could not be solved by existing schemes. To overcome the problems, we employ the chaotic system of a vertical-cavity surface-emitting laser (VCSEL) mutual coupling network to generate chaotic time series through optical system simulation and experimentation in this paper. Furthermore, a photonic reservoir computing based on VCSEL, along with a feedback loop, is proposed for the short-term prediction of the chaotic time series. The relationship between the prediction difficulty of the reservoir computing (RC) system and the difference in complexity of the chaotic time series has been studied with emphasis. Additionally, the attention coefficient of injection strength and feedback strength, prediction duration, and other factors on system performance are considered in both simulation and experiment. The use of the RC system to predict the chaotic time series generated by actual chaotic systems is significant for expanding the practical application scenarios of the RC.