Aiming at studying the influences of epilepsy on brain's nonlinear characteristics, we analyzed the difference between the normal EEG (electroencephalogram) and epileptic EEG from the perspective of nonlinear dynamics. Two sets of data used in this paper, including 16 cases of normal EEG and the same quantity of epileptic EEG, were from General Hospital of Nanjing Military Region. Firstly, on the basis of the Recurrence Plot (RP), the Order Recurrence Plot (ORP) was adopted to analyze two different kinds of EEG qualitatively. Then Average Diagonal Length, a parameter coming from Recurrence Quantification Analysis (RQA), was calculated to analyze the difference between normal EEG and epileptic EEG in nonlinear character, quantitatively. Compared with the healthy control subjects, the epileptic EEG is more regular and more certain, meanwhile, it's Average Diagonal Length is longer. Epilepsy makes patients' EEG become weaker in nonlinear chaotic characteristics but stronger in regularity and certainty.