A simple and cost-effective multi-wavelength fiber ring laser based on a chirped Moiré fiber grating (CMFG) and a semiconductor optical amplifier (SOA) is proposed. Stable triple-wavelength lasing oscillations at room temperature are experimentally demonstrated. The measured optical signal-to-noise ratio (SNR) reaches the highest value of 50 dB and the power fluctuation of each wavelength is less than 0.2 dB within a 1-h period. To serve as a wavelength selective element, the CMFG possesses excellent comb-like filtering characteristics including stable wavelength interval and ultra-narrow passband, and its fabrication method is easy and flexible. The lasing oscillation shows a narrower bandwidth than SOA-based multi-wavelength fiber lasers utilizing some other kinds of wavelength selective components. Methods to optimize the laser performance are also discussed.