We report highly efficient continuous-wave terahertz (THz) photoconductive antenna based photomixer employing nano-gap electrodes in the active region. The tip-to-tip nano-gap electrode structure provides strong THz field enhancement and acts as a nano-antenna to radiate the THz wave generated in the active region of the photomixer. In addition, it provides good impedance matching to the THz planar antenna and exhibits a lower RC time constant, allowing more efficient radiation especially at the higher part of the THz spectrum. As a result, the output intensity of the photomixer with the new nano-gap electrode structure in the active region is two orders of magnitude higher than that of a photomixer with typical interdigitated electrodes. Significant improvement in the THz emission bandwidth was also observed. An efficient continuous wave THz source will greatly benefit compact THz system development for high resolution THz spectroscopy and imaging applications.