Due to the increasing demand for small, low-cost, high-resolution radars, frequency-modulated continuous wave (FMCW) radars are gaining more and more attraction. One major challenge with the digital signal processing (DSP) employed in FMCW radars is reducing the number of required computations in order to achieve a real-time operation. Most FMCW radars need to continuously perform the Fast Fourier Transform (FFT) to determine the object range, velocity, etc. This computational burden is a major obstacle to the radar real-time operation. In this letter, a computationally efficient FMCW radar is proposed capable of reducing the number of required FFT operations without sacrificing the resolution of the estimated range. With careful selection of parameters, simulations show that the new method can reduce the number of required FFT operations by a factor of about 119 and 183 in two different scenarios when compared to a conventional solution.