Traditional single-pixel imaging uses Fourier patterns to modulate objects in the Cartesian coordinate system. The Cartesian Fourier pattern of single-pixel imaging is inappropriate to display in a circular field of view. However, a circular field of view is a widespread form of display in computed optical imaging. Here, circular patterns are adopted to adapt to the circular visual area. The circular patterns are displayed in polar coordinates and derived from two-dimensional Fourier transform in polar coordinates. The proposed circular patterns have improved imaging efficiency significantly from 63.66% to 100%. The proposed polar coordinate Fourier single-pixel imaging is expected to be applied in circular field-of-view imaging and foveated imaging.