A low complexity range-azimuth frequency-modulated continuous-waveform (FMCW) radar sensor using joint angle and delay estimation method without singular value decomposition (SVD) and eigenvalue decomposition (EVD) is presented in this paper. Conventional joint angle and delay estimation techniques exploit the dual-shift-invariant structure of received signals through matrix decompositions, such as SVD and EVD, which increases the computational burden. The proposed method utilizes the dual-shift-invariant structure through matrix inversion and performs angle and delay estimation using extended one-dimensional pseudospectrum searching instead of two-dimensional pseudospectrum searching to reduce the computational complexity. We demonstrate the effectiveness of the proposed method through Monte-Carlo simulations. The proposed algorithm is also verified by processing real FMCW data collected in an anechoic chamber.