Deep neural network (DNN) approaches have shown remarkable progress in automatic Chest X-rays classification. However, existing methods use a training scheme that simultaneously trains all abnormalities without considering their learning priority. Inspired by the clinical practice of radiologists progressively recognizing more abnormalities and the observation that existing curriculum learning (CL) methods based on image difficulty may not be suitable for disease diagnosis, we propose a novel CL paradigm, named multi-label local to global (ML-LGL). This approach iteratively trains DNN models on gradually increasing abnormalities within the dataset, i,e, from fewer abnormalities (local) to more ones (global). At each iteration, we first build the local category by adding high-priority abnormalities for training, and the abnormality's priority is determined by our three proposed clinical knowledge-leveraged selection functions. Then, images containing abnormalities in the local category are gathered to form a new training set. The model is lastly trained on this set using a dynamic loss. Additionally, we demonstrate the superiority of ML-LGL from the perspective of the model's initial stability during training. Experimental results on three open-source datasets, PLCO, ChestX-ray14 and CheXpert show that our proposed learning paradigm outperforms baselines and achieves comparable results to state-of-the-art methods. The improved performance promises potential applications in multi-label Chest X-ray classification.