Abstract: Based on the starlike function in classical geometric function theory, the class of q-starlike function which is related to q-derivative was studied in this paper. By applying Carathéodory-Toeplitz theorem, the coefficients of Carathéodory function were parameterized. With this contribution, the coefficients and its related Hankel determinants of q-starlike function were observed with the application of the relationship between classes of Carathéodory function and q-starlike function. The upper bounds of the coefficients and several Hankel determinants of q-starlike function are obtained in this paper.