The radiometer with spectrum analysis backend can be considered prototypical for spectrometer development for future radio astronomical applications. This paper focuses on the design and implementation of a Fast Fourier Transform(FFT) spectrum analysis backend for radiometer. The Kintex-7 family evaluation Field Programmable Gate Array(FPGA) of Xilinx Company with a 4 DSP FMC150 daughter card is the core to complete this system. The spectrometer works continuously and has a total bandwidth of 250 MHz，resolved into 16 384 channels with a frequency resolution of 15 kHz. The design scheme of delay-calibration for high speed data transmitting，pipelined, streaming I/O FFT structure，and spectrum accumulation modules，as well as software flowchart is presented. Finally, both simulation results obtained by Modelsim and MATLAB are compared to verify this system.