Single-mode cw lasing was obtained for the first time in Yb3+ : GGG crystals at room temperature at 1.030 and 1.037 μm upon pumping Yb3+ ions by a 0.925-μm neodymium-doped fibre laser. Lasing was observed at the transitions between the lower Stark sublevel of the 2F5/2 level and the upper Stark sublevels of the 2F7/2 ground state of Yb3+ ions. The study of lasing characteristic showed that lasing occurs according to the four-level scheme. The lasing threshold with respect to the absorbed power was 85 mW and the slope lasing efficiency was 20%. Upon 1.7-W pumping, the output power of 310 mW was achieved with the output resonator mirror with the transmission coefficient of 1%. The effective cross section of the lasing transition was 0.9×10-20 cm2.