In this paper, a tunable erbium-doped fiber random laser based on M-Z structure is proposed. The output process, the wavelength tunable output and the stability of random laser were experimentally studied. Two 2×2 optical fiber couplers were fused by optical fiber fusion to form an all-fiber M-Z filter structure. The experimental results show that the threshold power of the laser is 120 mW. The gain loss is changed by adjusting the tunable attenuator, and the wavelength tunable output is realized. The single-wavelength output is 1 554.4, 1555.2 and 1556.3 nm respectively, and the signal-to-noise ratio is 31.65 dB. The dual-wavelength output is 1 525.9, 1 556.2 and 1 531.6, 1 556.2 nm respectively, and the signal-to-noise ratio is better than 21.92 dB. The output of three wavelengths are 1 527.4, 1 546.9, 1 551.6 and 1 526.9, 1 530.0 and 1 549.8 nm respectively, and the signal-to-noise ratio is better than 20.10 dB. The four-wavelength output is 1 525.9, 1 530.1, 1 547.9 and 1 552.3 nm, and the signal-to-noise ratio is better than 18.95 dB. The stability of single wavelength and dual wavelength is better than 1.65 and 1.99 dB respectively. The slope efficiency of the laser is 0.627%. Therefore, the random laser can achieve single-wavelength, dual-wavelength, three-wavelength tunable output and four-wavelength stable output.