Optical and laser properties of a new Er/Yb-doped composite optical fiber manufactured according to the "rod-in-tube" technique are presented. The fabricated composite fiber with a standard outer diameter of 125 μm was single-mode at the wavelength of 1.55 μm. A Fabry-Perot laser cavity was manufactured on a 25 mm long fiber segment using the femtosecond technique of Bragg gratings inscription. The resulting laser with an effective cavity length of 12 mm generated strictly continuouswave single-frequency radiation at a wavelength of 1548.3 nm at room temperature (295 K). The key advantage of the studied Er/Yb-doped composite fiber laser is the excellent temporal stability of the laser output without any tendency for self-excited oscillation mode at any pump level.