In order to judge the state of secondorder chaos system more accurately and efficiently, in this paper, starting from the characteristic of Duffing oscillator and using the intensity of Poincare section points as the criterion of chaotic state, a quantitative description has been developed to distinct the state of chaotic by constructing a function. The method is mainly according to different periodic characteristic of second-order chaotic system showing in specific conditions. To obtain the Poincare section points, the system output is sampled as a constant period, which is all just the same to the period of the driving force. Based on the calculation to the deviation's mean square value of a fixed number of adjacent sampling points, this method indicates concentrate degree of the sampling points' distribution quantificationally. Then through the further experiment, an appropriate threshold can be determined and the chaotic state can be judged. The method directly uses the basic characteristics of chaos as the criterion to realize the chaotic state judgment from the system Poincare section's point, greatly reducing the computation complexity, weakening the effect of the machine error when computer numerically is calculating and the detection accuracy is increasing. The result shows that the sampling time is shortened, thus shortening the time of decision and improving the efficiency of decision. Through conducting an experiment by using the Duffing oscillator driven by Second order periodic force as an example, an anticipative conclusion is reached to prove the feasibility of the theory. By reproducing the experiments of former theory, and compared this theory to the former, this theory has higher accuracy and efficiency.