We study the problem of constructing confidence intervals for the long-memory parameter of stationary Gaussian processes with long-range dependence. The focus is on confidence intervals for the wavelet estimator introduced by Abry and Veitch (1998). We propose an approximation to the distribution of the estimator based on subsampling and use it to construct confidence intervals for the long-memory parameter. The performance of these confidence intervals, in terms of both coverage probability and length, is studied by using a Monte Carlo simulation. The proposed confidence intervals have more accurate coverage probability than the method of Abry and Veitch (1999), and are easy to compute in practice. Key words and phrases. Long-range dependence, resampling, wavelets, Hurst parameter.