This study presents a high-power, single-longitudinal-mode (SLM) fiber oscillator with a ring cavity design, operating at 1064 nm. Utilizing a double-cladding ytterbium-doped fiber as the gain medium, the system incorporates a fiber Bragg grating Fabry-Perot cavity and a dual coupler ring for step-by-step filtering to achieve SLM operation. With a pump power of 4.19 W, the oscillator delivered an output power of 1.01 W and narrowed the linewidth to 147 Hz, with the potential for further power increase. The oscillator demonstrated excellent longitudinal-mode stability, maintaining mode-hop-free operation for 8.7 hours after temperature stabilization. To the best of our knowledge, this work represents the longest duration of mode-hop-free operation and the narrowest laser linewidth achieved by a free-running ring-cavity SLM fiber oscillator at watt-level output powers.