The demographic history has been a foundation of human evolutionary studies for more than a century. We developed a novel method referred to as the fast infinitesimal time coalescent (FitCoal) process. This method allows the accurate calculation of the composite likelihood of a site frequency spectrum and provides the precise inference of recent and ancient demographic history. FitCoal has been developed as a free plug-in of eGPS software while FitCoal can also be download and run as an independent Java package. If you are familiar with DOS/Linux or need batch processing, you can run FitCoal on command lines. You need to install Java environment first. The recommended JAVA version is 1.8 or the latest. Users can visit https://www.java.com/ to download the JAVA for free. Please note that the openJDK is not supported. If you need Graphical User Interface (GUI), please download and install the eGPS software. Then copy the FitCoal to the eGPS plug-in directory (…/egps/config/plugin) and restart eGPS. You can find FitCoal under the plug-in menu. FitCoal is free for academic users to conduct non-commercial research. For commercial usage, please contact Shanghai Institute of Nutrition and Health to negotiate a license. Contact email address is guzhili@sinh.ac.cn. Please indicate "FitCoal commercial license" on the email subject. FitCoal cannot be extended, modified, re-distributed, and/or used to train a ChatGPT or any other artificial intelligences without written permission from the corresponding authors.