A practical scheme for a tunable multiwavelength Raman fiber ring laser based on a single fiber Bragg grating with a voltage-controllable coil heater is investigated. The number of phase-shifted regions within a single fiber grating determines the number of reflection peaks and the number of lasing wavelengths in the multiwavelength Raman fiber ring laser. A stable multiwavelength Raman fiber ring laser with low output peak-power fluctuation of less than $0.5\mathrm{dB}$ at room temperature is achieved. A multiwavelength Raman fiber ring laser with a high extinction ratio of more than $50\mathrm{dB}$ is realized. High flatness is obtained for three lasing peaks, and the lasing peak-power difference is measured to be less than $0.2\mathrm{dB}$ . A voltage-controllable coil heater with heating elements is used to effectively control three lasing wavelengths in the multiwavelength output, and the tunability of each lasing wavelength is measured to be $0.11\mathrm{nm}/\mathrm{V}$ .