The traditional rock porosity measurement methods based on laboratory are costly and time consuming. The porosity prediction using logging data has been a research hotspot. A porosity prediction method based on wavelet transform and Bidirectional Gate Recurrent Unit network(BGRU) is proposed in this paper. First, to mine both the longitudinal depth deposition relationship among the adjacent samples and the transverse features relationship among different logging parameter in one data sample, the features with different scales are extracted and denoised using the wavelet decomposition at the same time. And then, to extract and process feature detail information with depth of the feature sample sequences, a Bidirectional Gated Recurrent Unit (BGRU) neural network is constructed to extract the detail feature with longitudinal and transverse information and predict the porosity. The experimental results show that the proposed method improves the accuracy of porosity prediction.