We developed a 1.2 GHz bandwidth spectrometer based on combined complex FFT algorithm for radio astronomy. It resolves the contradiction between wide bandwidth and high speed real-time processing by using the combined complex FFT algorithm. Block-RAMs(BRAMs) in FPGA are saved by parallel processing and module multiplexing, while the computation time also decreases significantly due to symmetry properties of intermediate variables in data processing. Observations at Shanghai Astronomical Observatory for pulsars with the developed spectrometer show that the system works well and meets the requirements of the observation.