Most of the current research methods use the prediction correction method, but other numerical methods are less frequently used. In this paper, a numerical method for computing fractional-order dynamical systems is elaborated using Lagrange polynomial interpolation. And this is used to successfully obtain an effective numerical solution for a new fractional-order jerk chaotic system. The results obtained are compared with those of the prediction correction method and found to be in good agreement with each other, verifying the validity of this method. The maximum Lyapunov exponent of the new fractional-order jerk chaotic system is further explored for different system orders, and it is concluded that the system exhibits instability when the system order α=0.85, α=0.95, and the phase diagram of the system in Caputo’s sense is further demonstrated.The results show that different system order α have a significant effect on the dynamical behaviour of new fractionalorder jerk chaotic system.