Function-valued Padé-type approximation (FPTA) was applied to solve the Fredholm integral equations of the second kind. To avoid the constraint that the determinant of Hankel cannot equal to zero for FPTA, a definition and its construction of a function-valued Padé-Frobenius approximation (FPFA) is given. By studying the kernel structure of the Toeplitz matrix, an algorithm is presented for the function-valued Padé-Frobenious approximation with reduced denominator. Thus the application range of approximation solution of the integral equations is developed. Finally, an example is given to show effectiveness of the method.