Modern non-autoregressive (NAR) speech recognition systems aim to accelerate the inference speed; however, they suffer from performance degradation compared with autoregressive (AR) models as well as the huge model size issue. We propose a novel knowledge transfer and distillation architecture that leverages knowledge from AR models to improve the NAR performance while reducing the model's size. Frame- and sequencelevel objectives are well-designed for transfer learning. To further boost the performance of NAR, a beam search method on Mask-CTC is developed to enlarge the search space during the inference stage. Experiments show that the proposed NAR beam search relatively reduces CER by over 5% on AISHELL1 benchmark with a tolerable real-time-factor (RTF) increment. By knowledge transfer, the NAR student who has the same size as the AR teacher obtains relative CER reductions of 8/16% on AISHELL-1 dev/test sets, and over 25% relative WER reductions on Librispeech test-clean/other sets. Moreover, the ∼9x smaller NAR models achieve ∼25% relative CER/WER reductions on both AISHELL-1 and Librispeech benchmarks with the proposed knowledge transfer and distillation.