Abstract: Stationary long memory process has been widely studied in the literature. In this article, we considered the locally stationary long memory process with time-varying memory parameter. A new wavelet-based algorithm was developed using log-linear relationship between the wavelet coefficient variance and the scaling parameter. The consistency and the finite sample behavior of the estimator have also been studied, which provide a good reference for the practitioner and researchers. The new algorithm has also been applied to the YEN/USD exchange rate series, which leads to some interesting results.