Based on the maximum-entropy (ME) principle, a new power spectral estimator for random waves is derived in the form of ~S(ω)=(a/8)-H2(2π)d+1ω-(d+2)exp[-b(2π/ω)n], by solving a variational problem subject to some quite general constraints. This robust method is comprehensive enough to describe the wave spectra even in extreme wave conditions and is superior to periodogram method that is not suitable to process comparatively short or intensively unsteady signals for its tremendous boundary effect and some inherent defects of FFT. Fortunately, the newly derived method for spectral estimation works fairly well, even though the sample data sets are very short and unsteady, and the reliability and efficiency of this spectral estimator have been preliminarily proved.