Lack of typical fault samples remains a huge challenge for intelligent fault diagnosis of gearbox. In this paper, a novel approach named deep transfer multi-wavelet auto-encoder is presented for gearbox intelligent fault diagnosis with few training samples. Firstly, new-type deep multi-wavelet auto-encoder is designed for learning important features of the collected vibration signals of gearbox. Secondly, high-quality auxiliary samples are selected based on similarity measure to well pre-train a source model sharing similar characteristics with the target domain. Thirdly, parameter knowledge acquired from the source model is transferred to target model using very few target training samples. Transfer diagnosis cases for different fault severities and compound faults of gearbox confirm the feasibility of the proposed approach even if the working conditions have significant changes.