A Yb:GdVO4 single crystal was grown by the Czochralski process. Its thermal conductivity was measured by photothermal analysis and reached 8.1 and 7.1 W m(-1) K(-1) along and perpendicular to the c axis, respectively. These values are in good agreement with the predicted ones. The optical spectroscopy of the crystal, such as its absorption and emission cross sections under the two polarizations, its fluorescence lifetime, and its laser parameters, is investigated. Cw laser oscillation is obtained for what is to our knowledge the first time in this material under titanium sapphire pumping at 984 nm. We obtain 420 mW of output power for a 2% output coupler at 1029 nm. With a thin sample, the laser wavelength decreases to 1015 nm. In this case the quantum defect is as small as 2.9%. The weak heat release of the material suggests good prospects for its use in high-power applications.