In order to explore the difference of different light sources response to light source intensity fluctuation in reference-frame-independent quantum key distribution (RFI-QKD) protocol, a theoretical analysis and calculation scheme of RFI protocol key rate under imperfect light source is proposed. Through simulation, the performance of RFI-QKD protocol with weak coherence sources (WCS) is compared with that with heralded pair-coherent sources (HPCS) andheralded single-photon sources (HSPS) under intensity fluctuations with the common quantum communication parameters. The results show that compared with WCS, HSPS and HPCS have better performance and resistance to fluctuations under the same conditions, and predictable coherent light sources show best at any condition. It indicates that the proposed intensity fluctuation analysis scheme is realizable under RFI-QKD, and the simulation results can provide a valuable reference for parameterselection and optimization of RFI-QKD experimental research.