Whispering is an important mode of human speech, but no end-to-end recognition results for it were reported yet, probably due to the scarcity of available whispered speech data. In this paper, we present several approaches for end-to-end (E2E) recognition of whispered speech considering the special characteristics of whispered speech and the scarcity of data. This includes a frequency-weighted SpecAugment policy and a frequency-divided CNN feature extractor for better capturing the high-frequency structures of whispered speech, and a layer-wise transfer learning approach to pre-train a model with normal or normal-to-whispered converted speech then fine-tune it with whispered speech to bridge the gap between whispered and normal speech. We achieve an overall relative reduction of 19.8% in PER and 44.4% in CER on a relatively small whispered TIMIT corpus. The results indicate as long as we have a good E2E model pre-trained on normal or pseudo-whispered speech, a relatively small set of whispered speech may suffice to obtain a reasonably good E2E whispered speech recognizer.