By the order of the founding emperor of the Ming dynasty Zhu Yuanzhang 朱元璋 (1328-1398), a set of Zij was compiled and translated into Chinese during the Hongwu Reign (1368-1398) under the Chinese title Huihui lifa 回回曆法 (Chinese-Islamic System of Calendrical Astronomy).  Previous studies have provided us with a good picture about how the Zij was adopted in parallel with the official Chinese system, the Datong li 大統曆 (Great Union System of Calendrical Astronomy), and applied in astronomical calculations by the Muslim astronomers serving at the imperial observatory of Ming dynasty. This paper will try to move a little bit further to show how the Zij was looked upon and understood by Chinese astronomers in the Ming and Qing period. In view that the Zij contained some astronomical techniques that the Chinese astronomy did not cover, Chinese astronomers in the period kept a high opinion on Islamic astronomy. When the Datong li was found inaccurate, some of them even attempted to understand the scientific principles of the Zij in order to seek the inspiration for a calendar reform. With very little knowledge about the underlying astronomical theories of the Zij, their explanations and discussions of the Zij are full of misunderstandings and mistakes. In the end of the Ming dynasty, a systematic introduction of European astronomy into China brought about a correct understanding of the scientific principles of the Zij, but due to the lack of the knowledge about the cultural background for its development, an early imagination about its origin was activated and evolved into a cultural fantasy concerning the origin and dissemination of Indian, Islamic and European astronomy and religions.