A simple and novel solution is proposed to overcome the main beam splitting of the tapered slot antenna (TSA) fabricated on a thick substrate with high dielectric constant. It utilised arrays of metal strip gratings to reduce the undesirable surface waves. Measured result of a 10lambda0 long 35GHz linear taper slot antenna (LTSA), shows a dramatic improvement in the radiation pattern and a measured front-to-back ratio of 20dB for both the planes. Further analysis shows that the metal strip gratings help to improve the directivity and return loss of shorter LTSAs. Comparing with a basic LTSA without modification, the 4lambda0 LTSA has a 4.3dB and 14.8dB improvement on its directivity and return loss, respectively, which is 13.2dB and 22.3dB. In addition, the side lobe level is also suppressed from -5.2dB to -14.4dB. A new stepped profile formed by multiple constant slot width sections, to match the impedance between the feed and the aperture, is developed. This novel step-tapered profile increases the directivity of the antenna without increasing its length. A step-tapered slot antenna (STSA) is demonstrated at 28GHz. It has a directivity of 7.9dB, a 2.5dB improvement over a LTSA with the same physical design, and shows no sign of main beam splitting. With the incorporation of the metal strip gratings, the directivity of the STSA further increases to 11.0dB with a return loss of 17.2dB. Finally, an improved CPW-to-slotline transition is developed for the STSA. The above work helps to open up the TSA for commercial millimetre-wave applications, such as radio-over-fibre, satellite communications and remote sensing, which previously were not feasible due to the requirements of fragile and costly ultra thin substrate or micromachining.