In this paper, a pipelined frequency-modulated continuous-wave (FMCW) radar baseband processor applied to real-time applications is proposed and implemented in 40-nm CMOS technology. The FMCW radar signal processing time is analyzed according to the system specifications. On the basis of the theoretical analysis and systematic considerations, a pipelined baseband architecture with internal single-port static random access memory (SRAM) is employed. The baseband processor is mainly composed of two-dimensional fast Fourier transform (2D-FFT), two-dimensional constant false alarm rate (2D-CFAR), digital beam-forming (DBF), and memory control modules. The 2D-FFT module is structured with a pipelined scheme and avoids the waste of data transferring time between modules. The 2D-CFAR module is programmable for different applications. The designed address control is proposed to depose the edge cells. The processor occupies a core chip area of 3.353 mm ×3.353 mm and has been tested on the personal computer (PC) and field programmable gate array (FPGA) platform. The power consumption and processing time are also analyzed and compared with other works. The processor consumes 55.65 mW, including SRAMs. The processing time is 12.67 ms with the maximum window size and 256 targets when operating at 125 MHz. This time is estimated based on the assumption that each chirp lasts for 0.04096 ms, and data input takes 10.48 ms. Within this period, the range FFT is completed. The Doppler FFT, 2D-CFAR with the maximum window size, and DBF with 256 targets require 0.80 ms, 1.16 ms, and 0.23 ms respectively.