Nowadays, the health management of rotating machinery based on deep learning has achieved remarkable results. Nevertheless, in the presence of variable working conditions, the sparse nature of the valuable fault information makes the traditional deep models insufficient to achieve effective fault identification. Attributing to the aforementioned challenges, this research presented a new local-global neighborhood graph and sparse graph embedding deep-regularized autoencoder method (LGSDLRAE) framework for variable operating fault diagnosis (FD). More specifically, the FD scheme leverages manifold neighborhood graph embedding ability to mine fault information, combined with sparse theory ability in improving the generalization performance, to improve the performance of the original autoencoder (AE) algorithm. In the feature extraction (FE) phase, to enhance the compactness of homogeneous-classes and increase the separation between heterogeneous-classes by adopted global-local regularization terms; meanwhile, adding L1/2- sparse regularization terms gather the L1 regularization norm can make the data more sparse characteristics and L2 regularization norm prevents overfitting of data performance of the model and improve the generalization ability of the model. Finally, the identification accuracy of the datasets constructed variable operating conditions of double-span rotor test rig and planetary gearboxes are both above 98%, proving the superior performance of LGSDLRAE, respectively.