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We demonstrate the temperature distribution and 2.79 μ m laser performance in a high-quality Er:YSGG single crystal fiber (SCF) with size of Φ 0.85 × 8 mm3 for the first time. Compared with 2 × 2 × 8 mm3 Er:YSGG bulk crystal, the simulation results show that the center maximum temperature of Er:YSGG SCF is much lower, and the temperature rising and total thermal deformation are evidently reduced, indicating that the SCF possesses more efficient thermal dissipation. Under 970 nm laser diode pumping, a maximum output power of 636 mW with slope efficiency of 20.2% is realized. More importantly, a high beam quality factors M x 2 / M y 2 of 1.28/1.29 is obtained, which is close to the fundamental TEM 00 mode, suggesting that the Er:YSGG SCF can act as a promising candidate for mid-infrared laser seed source. • Er:YSGG single-crystal fiber(SCF) with a diameter of Φ 0.85 mm is prepared successfully. • Temperature distribution simulation shows the SCF possesses more efficient thermal dissipation. • 2794 nm CW laser power of 636 mW and beam quality factor M x 2 / M y 2 of 1.28/1.29 are achieved. • Er:YSGG SCF laser is a promising candidate for mid-infrared laser seed source. [ABSTRACT FROM AUTHOR]