As the seismic responses of unconventional hydraulic fracturing, downhole microseismic signals play an essential role in the exploitation of unconventional oil and gas reservoirs. In geologic structure interpretation and reservoir development, high-quality downhole microseismic data are necessary. However, the characteristics of downhole microseismic signals, such as weak energy and high frequency, bring great difficulty to signal-to-noise ratio enhancement. How to suppress the random noises in 3C downhole microseismic signals becomes problematic. To solve this problem, the 3D shearlet transform is introduced into downhole microseismic data processing. Different from the 2D shearlet transform, the correlation among the 3C of downhole microseismic signals is fully considered in the 3D shearlet transform, which enables the 3D shearlet transform to suppress random noise more effectively. In addition, for accurate selection of 3D shearlet coefficient, the back-propagation (BP) neural network is applied to the selection of coefficients. Unlike conventional threshold functions, BP neural networks can achieve optimal results by repeated training. At the same time, a new weight factor is proposed to improve the misconvergence of BP neural networks. Experimentally our method has been used to process synthetic and real 3C downhole microseismic signals, with results indicating that, compared with conventional methods, our new algorithm exhibits better performance in valid signal preservation and random noise suppression.