Although pre-trained big models (e.g., BERT, ERNIE, XLNet, GPT3 etc.) have delivered top performance in Seq2seq modeling, their deployments in real-world applications are often hindered by the excessive computations and memory demand involved. For many applications, including named entity recognition (NER), matching the state-of-the-art result under budget has attracted considerable attention. Drawing power from the recent advance in knowledge distillation (KD), this work presents a novel distillation scheme to efficiently transfer the knowledge learned from big models to their more affordable counterpart. Our solution highlights the construction of surrogate labels through the k-best Viterbi algorithm to distill knowledge from the teacher model. To maximally assimilate knowledge into the student model, we propose a multi-grained distillation scheme, which integrates cross entropy involved in conditional random field (CRF) and fuzzy learning. To validate the effectiveness of our proposal, we conducted a comprehensive evaluation on five NER benchmarks, reporting cross-the-board performance gains relative to competing prior-arts. We further discuss ablation results to dissect our gains.