Fractal is a new field of science to study the complexity and irregularity of events. The basic principles of fractal are introduced in this paper and used in the analyses of measles epidemics in Guangdong Province and Nanping district of Fujian Province, based on the monthly reported data on incidence, from 1951 to 1989. The results show that there are fractals in measles epidemics, the fractal dimensions are 1.588 and 1.626 before vaccination, and change to 1.716 and 1.758 after the vaccination respectively, indicating that the epidemics of mealses have become more complex and irregular than before. It is shown that fractal study is useful in expressing the complexity and irregularity of mealses epidemics.