Abstract: A multitaper spectral estimator is built based on the minimization of a cost function. It is indicated by the performance analysis that the approach here has comparative bias and variance as the approach of discrete prolate spheroidal sequence multitaper spectral analysis. Compared with the DPSS,instead of solving the problem of matrix eigenvalues, the multitaper in this paper needs less calculation with intuitionistic and analytical expression of tapers. The validity and the correctness of the approach are verified by the computer emulation of a discrete white noise sequence and an AR progress.