In this paper, a tunable erbium-doped fiber random laser based on M-Z structure is proposed, and the output process of random laser, the wavelength tunable output of random laser and the stability of random laser are experimentally studied. Two optical fiber couplers are fused by means of optical fiber fusion to form an all-fiber M-Z filter structure. The experimental results show that the threshold power of the laser is 120mW, the gain loss is changed by adjusting the tunable attenuator, and the wavelength tunable output is realized. The single-wavelength output is 1554.4nm, 1555.2nm and 1556.3nm respectively, and the signal-to-noise ratio is 31.65dB; The dual-wavelength output is 1525.9 nm, 1556.2 nm and 1531.6 nm, 1556.2 nm respectively, and the signal-to-noise ratio is better than 21.92 dB; The output of three wavelengths are 1527.4 nm, 1546.9 nm, 1551.6 nm and 1526.9 nm, 1530.0 nm and 1549.8 nm respectively, and the signal-to-noise ratio is better than 20.10 dB; The four-wavelength output is 1525.9 nm, 1530.1 nm, 1547.9 nm and 1552.3 nm, and the signal-to-noise ratio is better than 18.95 dB; The stability of single wavelength and dual wavelength is better than 1.65dB and 1.99dB 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.