Uyghur is a typical agglutinative language. It has a strong derivational ability with very a rich morphological structure and follows a harmonious rule. In the formation process, some phenomena may occur such as weakened, increased tone and fallen tone. The specific character of Uyghur language determines the difficulty of the Uyghur morphological analysis, including stemming and restoring the changed letter and POS tagging. This paper employs the hierarchical structure of Uyghur word, and proposes a directed graph model for Uyghur morphological analysis. In this model, words and tags are described as a directed graph. In this graph, nodes represent stems, affixes and their corresponding tags, while edges represent the transition, or general probabilities between nodes. Aimed at providing some light on the phenomenon of morphological sandhi in Uyghur language, this paper also proposes a restore model by changing the word to its original form. With the assumption that one letter can be changed to any letter, this model converts restoring problem into a sequence labeling problem, which could be solved by statistical methods. Experiment results on "Mega-words Corpus of Morphological Analysis of Uyghur", which is manually annotated by Xinjiang multilingual key laboratory shows that the accuracy of stemming reaches 94.7%, and the F score of stem and affix in line with tag reaches 92.6%.