Industrial production relies heavily on electric motors, but the motor vibration signals collected are often noisy, making it difficult to analyze the motor's performance. As a noise reduction method, the wavelet threshold has been used. However, the conventional methods of processing signals using soft and hard thresholds have issues such as the pseudo-Gibbs phenomenon and deviation in signal reconstruction. This paper proposes a solution to tackle the problems by introducing an algorithm that combines the variational mode decomposition (VMD) with a modified wavelet threshold noise reduction method. The improved sparrow search algorithm (SSA) is first applied to determine the optimal values of the number of modal components K and the penalty factor $a$. Then VMD decomposes the acquired motor vibration signal to obtain K intrinsic mode functions (IMF). Finally, the IMFs containing noise is processed by an improved wavelet threshold noise reduction method, which is used to obtain the noise-reduced signal after reconstruction. The effectiveness and superiority of the method proposed in this paper is verified by comparing with other methods in the experiments. The results show that the proposed noise reduction method effectively reduces noise interference in the motor vibration signal and is practical for use in industrial applications.