Text image machine translation (TIMT) aims at translating source language texts in images into another target lan- guage, which has been proven successful by bridging text image recognition encoder and text translation decoder. However, it is still an open question of how to incorporate fine-grained knowledge supervision to make it consistent between recognition and translation modules. In this paper, we propose a novel TIMT method named as BabyNet, which is optimized with hierarchical parental supervision to improve translation performance. Inspired by genetic recombination and variation in the field of genetics, the proposed BabyNet is inherited from the recognition and translation parent models with a variation module of which parameters can be updated when training on the TIMT task. Meanwhile, hierarchical and multi-granularity supervision from parent models is introduced to bridge the gap between inherited modules in BabyNet. Extensive experiments on both synthetic and real-world TIMT tests show that our proposed method significantly outperforms existing methods. Further analyses of various parent model combinations show the good generalization of our method.