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In this paper, we design the signal processing module based on FPGA for vehicle FMCW radar systems. We employ the detection algorithms based on two-step FFT (Fast Fourier Transform) using the several fast ramps in order to resolve radar range-velocity ambiguities. We implement the detection algorithms including the first FFT, DBF (Digital Beam Forming), the second FFT, and CFAR (Constant False Alarm) onto FPGA. In particular, the designed architecture supports multiple-receive channels to estimate target angles. The architecture also digitally generates a transmit wave using a DDS (Digital Direct Synthesizer) device. All algorithms and the controller are implemented into a Xilinx Virtex-5 platform and verified under the test platform.