In this paper, an algorithm is proposed for the identification of fractal signals with wavelet-based models from corrupted data. This algorithm is based on curve fitting and wavelet transformation. It is proved that whenever is greater than 0, the algorithm provides an almost consistent estimation. oreover, the estimated parameters are asymptotically Gaussian distributed. A mean-square asymptotic convergence rate of the estimated parameters has also been established. Simulation results verify the efficiency of the proposed algorithm.