We have developed a Watt-level random laser at 532 nm. The laser is based on a 1064 nm random distributed ytterbium-gain assisted fiber laser seed with a 0.35 nm line-width 900mW polarized output power. A study for the optimal length of the random distributed mirror was carried out. An ytterbium-doped fiber master oscillator power amplifier architecture is used to amplify the random seeder laser without additional spectral broadening up to 20 W. By using a periodically poled lithium niobate (PPLN) crystal in a single pass configuration we generate in excess of 1 W random laser at 532 nm by second harmonic generation with an efficiency of 9 %. The green random laser exhibits an instability <1 %, optical signal to noise ratio >70 dB, 0.1 nm linewidth and excellent beam quality.