We developed a 915-nm pumped, passively Q-switched 976-nm ytterbium all-fiber laser with an average output power of 4.3 W. The laser utilizes a 16-cm Yb gain fiber, passively Q-switched by a 1.8-cm Yb fiber, delivering stable single-mode pulses with an energy of 11.3 µJ at 0.38 MHz when pumped with 35 W. A slope efficiency of 16.4% was achieved. This work is the first, to our knowledge, demonstrated watt-level 976-nm Q-switched fiber laser without employing cascaded amplifiers. In addition, we established a set of coupled rate equations to model the system and forecast the potential for achieving higher output powers.