We report the demonstration of the first, to our knowledge, cladding-pumped continuous-wave Yb(3+)-doped phosphate-glass fiber laser. Phosphate hosts are of interest because they can be much more heavily doped than silica, and because of the possibility that they may have a higher photodarkening threshold. In an 84.6 cm double-clad fiber doped with 12 wt. % of Yb(2)O(3) and laser-diode pumped at 940 nm, nearly 20 W of single-mode 1.07 microm output power was generated with 60.2 W of absorbed pump power. The measured dependence of the output power on pump power is in excellent agreement with simulations.