A main line of research for introducing explanation capabilities in Knowledge-Based System supposes that explanations are used to transmit knowledge from the machine to a user and to improve learning ability of the latter. A reasonable explanation should be adapted to different level of users because different users have different knowledge. To describe the difference and then generate a personalized explanation is the main problem. In this paper, a novel method called FUMCE (Fuzzy User Model based Customized Explanation) is proposed, in which a fuzzy user model called FUM is defined, and then several new algorithms are proposed to initialize FUM, update FUM, and extract correlative knowledge for explanation based on the FUM. FUM-CE can provide different and suitable explanation for the different users with different domain knowledge, by which the understandability and acceptability of the expert system for earthquake prediction are improved.