As a modulation with relatively strong anti-interference capacity,quadrature phase shift keying(QPSK) has been extensively used in wireless satellite communication.This paper describes the Matlab simulation of QPSK demodulation,and designs an all-digital QPSK demodulation with FPGA.The core of demodulation is synchronization,which includes carrier synchronization and signal synchronization.The carrier synchronization is completed through numerical Costas loop,while signal synchronization through modulus square spectrum analysis,and the results are simulated on Matlab.The communication functions are implemented by upgradable or substitutable softwares as many as possible,based on the idea of software radio communication.The parameter values through Matlab simulation,combined with appropriate hardware system,technically realize the design of the proposed all-digital meteorological satellite demodulator based on FPGA.