Cross-domain Named Entity Recognition (NER) transfers the NER knowledge from high-resource domains to the low-resource target domain. Due to limited labeled resources and domain shift, cross-domain NER is a challenging task. To address these challenges, we propose a progressive domain adaptation Knowledge Distillation (KD) approach -- PDALN. It achieves superior domain adaptability by employing three components: (1) Adaptive data augmentation techniques, which alleviate cross-domain gap and label sparsity simultaneously; (2) Multi-level Domain invariant features, derived from a multi-grained MMD (Maximum Mean Discrepancy) approach, to enable knowledge transfer across domains; (3) Advanced KD schema, which progressively enables powerful pre-trained language models to perform domain adaptation. Extensive experiments on four benchmarks show that PDALN can effectively adapt high-resource domains to low-resource target domains, even if they are diverse in terms and writing styles. Comparison with other baselines indicates the state-of-the-art performance of PDALN.