A waveguide slot array antenna apparatus having a polarized wave plane in an oblique direction of a tube axis of a waveguide with proper excitation distribution of an aperture part for electromagnetic wave radiation or incidence. The waveguide slot array antenna apparatus is characterized by having a waveguide slot array antenna composed of a rectangular antenna waveguide whose cross section orthogonal to a tube axis is rectangular, wherein the antenna waveguide has a power feeding port at one end side in the tube axis direction, while the other end side is short-circuited. At a first wide plane of a pair of wide planes in parallel with the tube axis on the antenna waveguide, a plurality of elongated and rectangular (excluding square) apertures for electromagnetic wave radiation or incidence are arranged at intervals of about lambda g/2 (lambdag is intra-tube wavelength) along the tube axis. Each of the apertures has the same specified angle relative to a center line in parallel with the tube axis of the first wide plane, and adjacent apertures are arranged alternately at opposite positions relative to the center line. Each of the apertures at one side relative to the center line of the first wide plane is longer in length than about lambda f/2 (lambda f is free-space wavelength), while each of the apertures at the other side is shorter than about lambda f/2.