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Studying the carrier recombination process in MAPb(Br_1−yI_y)₃ single crystals (SCs) is important for its application in the optoelectronic field. In this work, a series of MAPb(Br_1−yI_y)₃ SCs with varied Br/I compositions have been studied. Steady-state photoluminescence (PL) spectra, time-resolved photoluminescence (TRPL) spectra and time-resolved microwave photoconductivity (TRMC) were used to understand the radiative and non-radiative recombination processes of MAPb(Br_1−yI_y)₃ SCs. By comparing the dynamics of TRPL and TRMC, we conclude that the dynamics of TRPL is dominated by the electron trapping process, which is in accordance with the fast decay component of TRMC kinetics, whereas the slower decay component in TRMC is dominated by the hole trapping process. Moreover, we find both the electron and hole trapping rates in mixed-halide perovskite MAPb(Br_1−yI_y)₃ (0 < y < 1) SCs are higher than that of mono-halide perovskite MAPbBr₃ SCs and MAPbI₃ SCs. This suggests mixed-halide crystals could introduce additional electron and hole trapping densities, which could be related to the fluctuation of Br/I compositions in the crystals. This work is helpful for understanding carrier recombination process in mixed-halide perovskite SCs.