A Tapered Slot Antenna (TSA) fed by a Coplanar Waveguide(CPW) on a high dielectric constant substrate (ε_r=11.9) worked at 35 GHz is presented. The performance of the TSA is sensitive to the effective thickness and electric constant of the substrate. In consideration of thin and fragile features of the high dielectric constant substrate for millimeter-wave application,a series of very closely spaced holes are formed on the substrate by using a deep etch technology,which synthesizes a localized low dielectric-constant environment and increases the effective thickness of the substrate. Otherwise,CPW-to-SLOT transitions with low insertion losses are proposed to feed this antenna. The simulation results show that the bandwidth and the gain of the antenna have been achieved 28.2% and 8.7 dB,respectively. After using micromachining technologies,the measured result shows the bandwidth is 13.2%. The difference between simulation and measurement is mainly attributed to the improvement for fabrication errors and measurement loads. This CPW-fed TSA has been expected to apply to communication systems for its easy integration with the uniplanar monolithic millimeter-wave integrated circuits.