Long computation time is required for transient stability analysis of power systems because it can be expressed as combination of differential and algebraic equations. In order to finish the calculation within a practical amount of time, it is an effective approach that applying Parareal method as one of parallel computing technique to transient stability analysis. In the Parareal method, the accuracy of the result is gradually updated through iterative procedures in combination with rough estimation of entire waveform and detailed calculation for each decomposed time window. Based on the Parareal method, the authors have developed a new stability assessment method by using chaos theory. If an operating point is in unstable region, the trajectory has the chaotic property, 'sensitive dependence on initial conditions'. Therefore, it is possible to assess the stability by detecting the convergence characteristics of the estimated waveform at each iterative procedure by the Parareal method. The effectiveness of the proposed method was tested by using IEEJ WEST10 system model. © 2016 IEEE.