Multiwavelength Brillouin erbium-doped fiber lasers with wavelength spacing of double and triple Brillouin frequency shifts are reported, and the multiwavelength tunable lasers are realized through changing the Brillouin pump wavelength. The experimental results show that eight Brillouin wavelengths with wavelength spacing 0.17 nm of double Brillouin frequency shifts are generated, and the wavelength can be tuned in a range of 110 nm (1528-1638 nm). Meanwhile, five Brillouin wavelengths with wavelength spacing 0.26 nm of triple Brillouin frequency shifts are obtained, and the wavelength can be tuned in a range of 60 nm (1535-1595 nm). Additionally, the experimental results also indicate that the Brillouin wavelength number can reach the maximum when the wavelength of the Brillouin pump laser is in the range of the self-excited oscillation. This tunable multiwavelength Brillouin fiber laser with multiple Brillouin frequency shift interval has important applications in many fields, including dense wavelength division multiplex optical fiber communication system, microwave signal generation, optical fiber sensing, and spectrum measurement.