To restore the continuum and the spectral lines from a noisy astronomical spectrum, then to measure the equivalent widths of the spectral lines, the fractal denoising method was firstly used in astronomical spectra in the present paper. The method is based on the distinguishing features, that is the local self-similarities exist in an astronomical spectrum, while not in a random white noise signal. The experimental results show that the fractal denoising method is efficient in parameter measurements, such as equivalent widths for spectral lines, redshift of galaxies, and so on. In addition, the method can achieve data compression. The fractal method can be used in the mass spectra of LAMOST.