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We demonstrated a novel graphene Q-switched erbium-doped fiber laser with wide pulse-repetition-rate range. The Q-switched fiber laser is constructed with a 37-cm linear cavity formed by two fiber Bragg gratings, a section of highly doped erbium fiber, and a graphene saturable absorber. The laser has a low pump threshold of 16.9 mW, a wide range of repetition rate from 31.7 to 236.3 kHz, and minimum pulse duration of 206 ns. The short-cavity laser structure enables laser action free of self-mode-locking effects.