The concept of using a low dielectric medium in a parallel-plate H-guide to obtain velocity-matching between optical and microwave signals for the LiNb03 modulator is analyzed in detail. From solutions of the wave equations, we have obtained characteristics of the fundamental mode and the design parameters which lead to velocity-matching. The mode is guided by the electrooptic substrate and decays exponentially outside the LiNb01 substrate. The parameter which determines itsproperties is 2a/A , i.e., width of the LiNbO3 substrate divided by the wavelength of the modulation signal. The phase velocity is dispersive, therefore, for a specific substrate width, velocity matching occurs only at a specific modulation frequency. A modulator built with such a velocity-matched electrode is expected to have only a finite bandwidth centered around the design frequency. Details of the analysis and characteristics of the H-guide are discussed in this paper.