The iteratively regularized Gauss-Newton method is applied to compute the stable solutions to nonlinear ill-posed problems F(x) = y when the data y is given approximately by y δ with ∥y δ - y∥ ≤ δ. In this method, the iterative sequence {x k δ } is defined successively by x k +1 δ = x k δ -(α k I + F' (x k δ ) * F' (x k δ )) -1 (F'(x k δ ) * (F(x k δ )-y δ ) + α k (x k δ - x 0 )), where x 0 δ := x 0 is an initial guess of the exact solution x and {α k } is a given decreasing sequence of positive numbers admitting suitable properties. When x k δ is used to approximate x , the stopping index should be designated properly. In this paper, an a posteriori stopping rule is suggested to choose the stopping index of iteration, and with the integer k δ determined by this rule it is proved that ∥x k δ - x∥ ≤ C inf {∥x k - x ∥ + δ/√αk∥: k = 0,1,...} with a constant C independent of δ, where x k denotes the iterative solution corresponding to the noise free case. As a consequence of this result, the convergence of x kδ δ is obtained, and moreover the rate of convergence is derived when x 0 - x satisfies a suitable source-wise representation. The results of this paper suggest that the iteratively regularized Gauss-Newton method, combined with our stopping rule, defines a regularization method of optimal order for each 0 < v < 1. Numerical examples for parameter estimation of a differential equation are given to test the theoretical results.