Abstract: Matlab software was applied to investigate a problem in implementing the Runge-Kutta method to simulate limit cycles of nonlinear dynamical systems. This problem refers to a misjudgement of the period of limit cycle oscillation, more specifically, a period-1 solution would possibly be considered to be period-2 or period-3. The relative errors of the results can be adjusted when directly calling the Matlab programs such as ode45. Taking the strongly nonlinear flutter system of an airfoil as an example, it revealed that, a period-1 limit cycle could be erroneously simulated as a period-2 or period-3 one. The correct solution can be obtained by improving the relative accuracy. This 〖JP3〗study demonstrates that it is worthy of paying more attention to the accuracy of the Runge-Kutta method, especially when used in simulating limit cycles.〖JP〗