We present a theoretical and experimental analysis of a diode-pumped Yb3+-doped Ca4GdO(BO3)(3) (Yb:GdCOB) laser. A new model for a diode-pumped quasi-three-level laser is described, The effects of absorption saturation, temperature profile, and the beam quality M-2 factor of the pump diode have been taken into account, for the first time to our knowledge. We have obtained a good agreement between experimental measurements and theoretical calculations with two different pump wavelengths, 902 and 976 nm, Our model has given good predictions of the laser performances for different crystal temperatures and different M-2 factors of the pump beam. As much as 440 mW of output power (at 1082 nm) have been achieved for 640 mW of absorbed pump power at 976 nm, corresponding to one of the highest slope efficiencies (81%) ever obtained with Yb-doped lasers.