Islamic Jamal al–Din zij and Chinese Shoushi-li(授時曆) are astronomical hand books compiled by Jamal al-Din(札馬 魯丁) and Guo Shujing(郭守敬) of the Islamic and Chinese Astronomical Bureau in Yuan(元) China, respectively. Jamal al-Din zij is an Islamic zij based on the Almagest of Ptolemaios, while Shoushii-li is a calendrical treatise by the traditional Chinese calendar system. In case of the parallax correction method, however, both of them have a common origin from Indian astronomy in 6-7 Century. This paper examines and discusses the parallax theory and its origin adopted in Jamal al–Din zij and Shoushi-li as following: 1) Definitions of the parallax theory and parallax correction methods. 2) Similarities and origins of the parallax correction methods adopted in the Jamal al–Din zij and Shoushi-li. 3) Comparison of the parallax correction tables included in the Sanjufini zij of Tibet, the Huihui-lifa(回回曆法) of Ming(明) China and the Chiljeongsan-Oepyeon(七政算外篇) of Joseon(朝鮮) Korea. 4) Routes of the parallax theory transmitted from ancient Greece and India to Joseon via Islam world and China, respectively. 5) Astronomical exchanges and mutual influence between the East and the West.