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With the rapid development of satellite mobile communication systems in recent years, high transmission rate, wide coverage, low transmission delay and strong flexibility are the requirements for the development of the new generation of 5G LEO satellite mobile communication systems. However, due to the high speed of the low orbit satellites, the larger Doppler shift is generated. By establishing a new low orbit satellite mobile communication system using 5G candidate waveform filtering orthogonal frequency division multiplexing (F-OFDM), a new Doppler frequency offset estimation method is designed for the new system. First, the Doppler characteristic of satellite orbit is used to calculate the integer Doppler frequency offset, and the second step is using the pilots information in the F-OFDM resource block to estimate the accurate Doppler shift. The pilot information is used to estimate the exact Doppler shift. This paper mainly completes the model of 5G low orbit satellite mobile communication system and the simulation of the algorithm in the system to verify its actual performance. The algorithm performance can be obtained through simulation, compared with the similar algorithm, the algorithm has low complexity and high accuracy.