The converse problem of Gaussian quadrature refers to the recovery of the Jacobi matrix from the quadrature formula. In other words, to solve the converse problem of Gaussian quadrature means to calculate the moments \(\int x^nd\mu(x)\) from the formula \(Q_n(f)= \sum^n_{k=1} \lambda_{n, k}f(x_{n,k})\). This paper presents a new algorithm based on the quotient-difference (qd) algorithm, which uses the relationship between the qd algorithm and continued fractions, namely the \((n-1,n)\) Padé approximants, associated to the Cauchy transform \(\widehat\mu(z)= f(z- x)^{-1} d\mu(x)\). The process of calculations of the present algorithm is faster than the Gragg-Harrod algorithm and is forward stable. A numerical example is given.