In this work the electrodynamic analysis of electromagnetic fields of TE-modes and surface currents density in walls of an asymmetric single-ridge waveguide and simulation of slot antenna array on its basis are presented.  The asymmetries caused by shift of a ridge from the symmetry plane of the waveguide and by the different sizes of groove areas of the single-ridge waveguide were considered. For calculation of electromagnetic fields and cutoff wave numbers of TE-modes in an asymmetric single-ridge waveguide with air filling the method of partial regions including field singularity at the edge was used. In the simulation process the perspective design of the slot antenna containing eight narrow slots, located on the center of a wide wall of the waveguide was investigated and optimized. The directional pattern of the slot antenna was optimized by reflection and side lobe level. The main lobe angular width is 110and side lobe level is lower than -27 dB.