We report, to the best of our knowledge, the first CW bismuth-doped fiber laser operating at around 1.31 μm with an output power of >1 W utilizing a cladding-pumping configuration with multimode semiconductor laser diodes emitting at a wavelength of 793 nm. The Bi-doped fiber (BDF) serving as an active medium of the laser was based on a pedestal-index design, where P2O5−SiO2 glass core surrounded by P-doped cladding. The BDF construction offers advanced gain characteristics and an increased mode size (∼13 μm). The fiber preform was fabricated by the conventional modified chemical vapor deposition (MCVD) method combined with all gas-phase doping technique. The BDF with low-index polymer coating provided sufficient cladding peak absorption at 750 nm belonging to bismuth active centers associated with phosphorus atoms (BACs-P) that allowed to develop a continuous-wave laser with a linear cavity configuration and enable a maximum slope efficiency of ∼ 4% with respect to the absorbed pump power. In addition, near-field spatial intensity distribution of optical beam has good quality (M2<1.13) and close to Gaussian mode profile in x and y directions. The perspectives for optimization of BDF design and laser system configurations based on such fibers for further power scaling are discussed.