To understand process executed in many activities, process mining technologies are now extensively studied. However, three major problems in the current process mining techniques are identified. First, most process mining techniques mainly use local search strategy to generate process models. Second, time intervals between two actives are not considered so that patterns that are different in view of time are regarded as the same behaviors. Third, no precision evaluation measure is defined to evaluate the quality of process models. To solve these difficulties, this research proposes a time-interval process mining method. A genetic process mining algorithm with time-interval consideration is developed. Then, a precision evaluation measure is defined to evaluate the quality of the generated process models. Finally, the best process model with highest precision value is reported.