In this paper, we propose a novel method for fault diagnosis in micro-electromechanical system (MEMS) inertial sensors using a bidirectional long short-term memory (BLSTM)-based Hilbert–Huang transform (HHT) and a convolutional neural network (CNN). First, the method for fault diagnosis of inertial sensors is formulated into an HHT-based deep learning problem. Second, we present a new BLSTM-based empirical mode decomposition (EMD) method for converting one-dimensional inertial data into two-dimensional Hilbert spectra. Finally, a CNN is used to perform fault classification tasks that use time–frequency HHT spectrums as input. According to our experimental results, significantly improved performance can be achieved, on average, for the proposed BLSTM-based EMD algorithm in terms of EMD computational efficiency compared with state-of-the-art algorithms. In addition, the proposed fault diagnosis method achieves high accuracy in fault classification.