In the present work, we consider the Toeplitz matrices whose elements are coefficients of functions of analytic functions and by making use of the Toeplitz determinant, we give some sharp estimates for Toeplitz determinant Tq(n) for low values of n and q when f belong to a class of functions in S∗(ψ). Further, we also find the Hankel determinant for the above class of functions which improves the recent result obtained by Raina and Sokol [6].