Machine translation is the process of translating text from one human language to another using a computer. It has gained much attention currently. Neural machine translation approaches are the current state of the art for machine translation that uses artificial neural networks. The sub-word level machine translation between the Afan Oromo language and Amharic language pair was proposed in this work. The study was carried out by investigating the capabilities of deep learning approaches on the algorithm of RNN (LSTM) with attention and Transformer model. A total of 20k parallel sentences are used for the experiment with a percentage split of 80% for training and 20% for testing. The experiment was conducted to compare the performance of two models and select the better model for Afan Oromo-Amharic -Amharic language machine translation. Bleu score evaluation metrics have been used to compare the performance of the two models. The result scored from the experiment with BLEU scores of 18.5% and 21.2% by the transformer model when translating from Afan Oromo to Amharic and from Amharic to Afan Oromo, respectively. While using the RNN (LSTM) model, we got a bleu score of 8.72% and 10.39% from Afan Oromo to Amharic and from Amharic to Afan Oromo, respectively. Therefore, it is concluded that the transformer model was better in bleu score performance in both directions for languages Afan Oromo and Amharic languages than the RNN (LSTM) model. The transformer model reduces memory needed for training, and training time and performs best result even if the length of the sentence increases when compared to LSTM.