In this paper, we introduce an end-to-end Amharic text-line image recognition approach based on recurrent neural networks. Amharic is an indigenous Ethiopic script which follows a unique syllabic writing system adopted from an ancient Geez script. This script uses 34 consonant characters with the seven vowel variants of each (called basic characters) and other labialized characters derived by adding diacritical marks and/or removing parts of the basic characters. These associated diacritics on basic characters are relatively smaller in size, visually similar, and challenging to distinguish from the derived characters. Motivated by the recent success of end-to-end learning in pattern recognition, we propose a model which integrates a feature extractor, sequence learner, and transcriber in a unified module and then trained in an end-to-end fashion. The experimental results, on a printed and synthetic benchmark Amharic Optical Character Recognition (OCR) database called ADOCR, demonstrated that the proposed model outperforms state-of-the-art methods by 6.98% and 1.05%, respectively.