Single-mode surface-emitting terahertz quantum cascade lasers with second-order concentric-circular-gratings are firstly demonstrated. The gratings are designed for single-mode operation and surface emission for efficient and directional optical power out-coupling. The first structure exhibits single-mode operation over the entire dynamic range with a side-mode-suppression-ratio of around 30 dB, and a six-fold rotationally symmetric far-field pattern, while a modified structure demonstrates single-mode operation with an improved beam divergence, whose far-field patteren consists of two lobes, each of which has a beam divergence within 13.5°×7° (full-width at half-maximum, FWHM). In addition, the devices show a peak output power approximately three times higher than in conventional ridge-waveguide lasers of similar size, whilst maintaining similar threshold current densities and maximum operating temperatures.