Tandem pumping technique are traditionally adopted to develop > 3-kW continuous-wave (cw) Yb3+-doped fiber lasers, which are usually pumped by other fiber lasers at shorter wavelengths (1018 nm e.g.). Fiber lasers directly pumped by laser diodes have higher wall-plug efficiency and are more compact. Here we report two high brightness monolithic cw fiber laser sources at 1080 nm. Both lasers consist of a cw fiber laser oscillator and one laser-diode pumped double cladding fiber amplifier in the master oscillator-power amplifier configuration. One laser, using 30-mu m-core Yb3+-doped fiber as the gain medium, can produce > 5-kW average laser power with near diffraction-limited beam quality (M-2<1.8). The slope efficiency of the fiber amplifier with respect to the launched pump power reached 86.5%. The other laser utilized 50-mu m-core Yb3+-doped fiber as the gain medium and produced > 8-kW average laser power with high beam quality (M-2: similar to 4). The slope efficiency of the fiber amplifier with respect to the launched pump power reach 83%. To the best of our knowledge, this is the first detailed report for > 5-kW near-diffraction-limited and > 8-kW high-brightness monolithic fiber lasers directly pumped by laser diodes.