The sound velocity profile is the base of various underwater acoustic equipment. In this paper, a low-cost sound velocity profiler is designed based on the time difference method. It mainly includes three parts: the control unit, the storage module and the ultrasonic measurement module. Its overall volume is small, and the standby power consumption is low. It can be integrated into various underwater measurement platforms and profilers to realize the sound velocity measurement, and it also could be used as a self-contained sound velocity sensor. Furthermore, according to the sound velocity measurement principle and response characteristics, a calibration algorithm based on Recurrent Neural Network (RNN) and Discrete Wavelet Transformation (DWT) is proposed, which can improve the accuracy and adapt to the nonlinear response of the system by using multiple sets of time data obtained from the measurements. It is verified by calibration experiments that the neural network calibration algorithm can effectively reduce the nonlinear system error in the measurement, and its effect is better than the traditional linear regression method. The designed system prototype can achieve measurement accuracy of 0.05m/s after calibration, which can meet the needs of low-cost and high-precision underwater sound velocity measurement.