Continuous wave (CW) radiation from a Yb-fiber laser (central wavelength 1064 nm, power 1-200 W) was used to initiate ablation of a gold target in deionized water and to synthesize bare (unprotected) gold nanoparticles. We show that the formed nanoparticles present a single low-size-dispersed population with a mean size of the order of 10 nm, which contrasts with previously reported data on dual populations of nanoparticles formed during pulsed laser ablation in liquids. The lack of a second population of nanoparticles is explained by the absence of cavitation-related mechanism of material ablation, which typically takes place under pulsed laser action on a solid target in liquid ambience, and this supposition is confirmed by plume visualization tests. We also observe a gradual growth of mean nanoparticle size from 8-10 nm to 20-25 nm under the increase of laser power for 532 nm pumping wavelength, whereas for 1064 nm pumping wavelength the mean size 8-10 nm is independent of radiation power. The growth of the nanoparticles observed for 532 nm wavelength is attributed to the enhanced target melting and splashing followed by additional heating due to an efficient excitation of plasmons over gold nanoparticles. Bare, low-size-dispersed gold nanoparticles are of importance for a variety of applications, including biomedicine, catalysis, and photovoltaics. The use of CW radiation for nanomaterial production promises to improve the cost efficiency of this technology.