Provided is a waveguide slot array antenna apparatus having a polarized wave plane in a direction oblique to a tube shaft of a waveguide, in which an excitation distribution of opening portions for radiating or receiving electromagnetic waves is appropriately attained. The waveguide slot array antenna apparatus includes a waveguide slot array antenna formed of a rectangular antenna waveguide which has a rectangular section orthogonal to a tube axis, in which: the rectangular antenna waveguide has one end side thereof in a tube axial direction serving as a feeding port and another end side short-circuited; the antenna waveguide has a plurality of slender rectangular opening portions for radiating or receiving an electromagnetic wave arranged at intervals of about »g/2 (»g is an intra-tube wavelength) along the tube axis on a first wide plane of a pair of wide planes that are parallel to the tube axis; the plurality of slender rectangular opening portions each have the same predetermined angle with respect to a center line parallel to the tube axis of the first wide plane; the opening portions adjacent to one another are alternately arranged at opposite positions with respect to the center line; the opening portions located on one side with respect to the center line of the first wide plane each have a length longer than about »f/2 (»f is a free space wavelength), and the opening portions located on another side each have a length shorter than about »f/2.