A tunable and switchable multi-wavelength random fiber laser (MW-RFL) is proposed and experimentally demonstrated in this work, which consists of a random distributed feedback mechanism, an improved Lyot filter, and a nonlinear optical loop mirror (NOLM). The theoretical derivation and simulation analysis of the improved Lyot filter are carried out by using the transfer matrix theory. The results show that by adjusting the polarization controller (PC) in the filter, not only the channel interval can be switched between 0.9 and 0.45 nm, but also the extinction ratio (ER) of the transmission spectrum can be adjusted and the wave peak position can be moved. The feedback mechanism of the proposed laser is provided by the randomly distributed backward Rayleigh scattering generated in the single-mode fiber. By changing the pump laser power, the number of output laser channels will be linearly increased. When the channel interval is kept constant, the wavelength can be tuned within a certain range by carefully adjusting the PC3 in the NOLM. When the channel interval of the spectrum is 0.9 nm, the wavelength tuning ranges of the three and four laser channels are 3.6 and 3.5 nm, respectively. When the channel interval of the spectrum is 0.45 nm, the wavelength tuning ranges of the three and four laser channels are 2.8 and 2.77 nm, respectively. Then the variations of the output spectrum when using 25 km single-mode fiber (SMF) are studied. It is observed that the linewidth and side mode suppression ratio (SMSR) of the laser channel are significantly increased. Finally, the stability of the random laser is discussed, and the maximum central wavelength drift and peak power fluctuation measured at room temperature are 0.05 nm and 0.34 dB, respectively. The average peak power and SMSR are maintained at −4.47 dBm and 34.6 dB, respectively, which confirms that the laser has good stability.