This paper initially introduces analytical solutions to newly invented inverted microstrip gap waveguide (IMGW). By applying the classical variational method the characteristic impedance, dielectric loss and conductor loss of the IMGW are obtained. The calculated characteristic impedance and losses of IMGWs with the present analytical method have been verified by commercial software CST. Furthermore, we have theoretically proved that the total loss of electromagnetic energy in the IMGW is much lower than that of covered microstrip line in millimeter waves (mmWs). Thereby, the IMGW has big advantages over covered microstrip lines for high-gain, high-efficiency array antennas in mmWs.Index Terms-inverted microstrip gap waveguide, variational method, Green's function, characteristic impedance, dielectric loss and conductor loss.Jinlin Liu (M'17) received the B.Sc. degree in Communications Engineering from the University of . He has authored and coauthored about 60 journal articles and about 150 conference papers, and more than 10 granted patents. His research interests include 60-140GHz antennas, terahertz antennas, MIMO antennas, ultra-wideband (UWB) antennas and UWB feeds for reflector antennas, UWB radar systems, UWB antennas in near-field sensing applications, hat-fed antennas, reflector antennas, radome design, and computational electromagnetics.Ashraf Uz Zaman (M'14) was born in Chittagong, Bangladesh. He received the B.Sc. degree in electrical and electronics engineering from the Chittagong University of Engineering and Technology, Chittagong, and the M.Sc. and Ph.D. degrees from the Chalmers University of Technology, Gothenburg, Sweden, in 2007 and 2013, respectively. He is currently an Assistant Professor with the Communication and Antenna Systems Division, Chalmers University of Technology. His current research interests include millimeter-wave planar antennas in general, gap waveguide technology, frequency-selective surfaces, microwave passive components, and packaging techniques and integration of MMICs with the antennas.