A real stationary Gaussian stochastic sequence with absolutely continuous spectral density f is considered. Let \(L_ n(f)\) be the Toeplitz approximation of its likelihood functional based on a sample of size n [cf. the second author and \textit{G. Szegö}, Toeplitz forms and their applications. (1958; Zbl 0080.095)]. The proposed estimator for f belongs to the sieve type estimators (ibid.) and is defined as a solution of the maximizing problem \(\max_ f L_ n(f)\) on the set of all functions g \((>0)\) with \(\| g^{(p)}| L^ 2(-\pi,\pi)\| <1/\mu (n),\) where \(p=1\) or \(=2\) and \(\mu\) (n)\(\to \infty.\) Theorems: The estimator is strongly \(L^ 1\)-consistent for \(\mu (n)=cn^{\delta -1}\), \(0<\delta <1\). If in addition \(\| (1/f)^{(i)}| L^ 2(-\pi,\pi)\| <\infty\) for \(0\leq i\leq p\) then the estimator is \(L^{\infty}\)-consistent.