High-frequency surface wave radar (HFSWR) is a useful technology for remote sensing of surface currents. It usually requires two (or more) stations spaced apart to create a two-dimensional (2D) current vector field. However, this method can only obtain the measurements within the overlapping coverage, which wastes most of the data from only one radar observation. Furthermore, it increases observation’s costs significantly. To reduce the number of required radars and increase the ocean area that can be measured, this paper proposes an economical methodology for remote sensing of the 2D surface current vector field using single shipborne HFSWR. The methodology contains two parts: (1) a real space-time multiple signal classification (MUSIC) based on sparse representation and unitary transformation techniques is developed for measuring the radial currents from the spreading first-order spectra, and (2) the stream function method is introduced to obtain the 2D surface current vector field. Some important conclusions are drawn, and simulations are included to validate the correctness of them.