The paper studies testing for the nonlinearity of a LSTAR model based on the transformed function with logistic form. Specifically, a simple linear model can be used to approximate the LSTAR model by Taylor expansion. For the two different models, the null hypothesis has been verified to be equivalent and then the corresponding hypothesis test can be more easily carried out. The research on its nonlinearity testing shows that to test the nonlinearity of this kind of LSTAR models, we need only replace the transition function with its first-order Taylor approximation, which can help us save many degrees of freedom. Monte Carlo simulation studies and real data applications show the usefulness of these theory results.