A compensation method for a magnetoelectric velocity sensor (MVS) is always necessary, which can lower the resonance frequency of the measuring system and subsequently extend the measuring bandwidth. In this paper, a novel compensation method is proposed based on the BP neural network under the TensorFlow architecture. Comparing with the existing methods, the new method does not depend upon an accurate model of the MVS any more, whose parameters are badly influenced by the temperature. The dynamic compensator is connected with the sensor. The BP neural network algorithm is used to identify compensation parameters. The dynamic compensator works at state of the optimum parameter all the time to compensate the dynamic performance of MVS by training the weights and thresholds of the neural network. The experiment results show that velocity measurement deviation is within ±5% error band by the dynamic compensator, which can reduce the measurement deviation caused by the variation of temperature and improve the measurement accuracy. The bandwidth can be as low as 0.28Hz. The dynamic compensator is superior to Random Forests and RBF Neutral Network in implement in FPGA/CPLD. Its' accuracy is superior to zero-pole compensation method. This method leads a new way to weaken the temperature variation characteristics of the velocity sensor and improve the measurement performance. INDEX TERMS Velocity sensor, bandwidth expansion, temperature dependence, BP neural network.