Mongolian morphological segmentation is regarded as a crucial preprocessing step in many Mongolian related NLP applications and has received extensive attention. Recently, end-to-end segmentation approaches with long short-term memory networks (LSTM) have achieved excellent results. However, the inner-word features among characters in the word and the out-word features from context are not well utilized in the segmentation process. In this paper, we propose a neural network incorporating inner-word and out-word features for Mongolian morphological segmentation. The network consists of two encoders and one decoder. The inner-word encoder uses the self-attention mechanisms to capture the inner-word features of the target word. The out-word encoder employs a two layers BiLSTM network to extract out-word features in the sentence. Then, the decoder adopts a multi-head double attention layer to fuse the inner-word features and out-word features and produces the segmentation result. The evaluation experiment compares the proposed network with the baselines and explores the effectiveness of the sub-modules.