We demonstrate a bidirectional fiber laser with an artificial saturable absorber of a step-index multimode fiber sandwiched by single-mode fibers. Two asynchronous noise-like pulse sequences with a repetition frequency difference of 3.16 kHz are obtained. The average power of the bidirectional asynchronous noise-like pulses is greater than 36 mW, and the pulse energy is greater than 3 nJ. The laser we demonstrate has potential applications in micromachining, supercontinuum spectrum generation, and signal processing.