In this paper, a new efficient adaptive filtering algorithm belonging to the Quasi-Newton (QN) family is proposed. In the new algorithm, the involved inverse Hessian matrix is approximated by a proper expansion, consisting of powers of a Toeplitz matrix. Due to this formulation, the algorithm can be implemented in the frequency domain (FD) using the fast Fourier transform (FFT). Efficient recursive relations for the frequency domain quantities updated on a step-by-step basis have been derived. The proposed algorithm turns out to be particularly suitable for adaptive channel equalization in wireless burst transmission systems. Based on this approach, new adaptive linear equalization (LE) and decision feedback equalization (DFE) algorithms have been developed. These algorithms enjoy the combined advantages of QN formulation and FD implementation, exhibiting faster convergence rate than their stochastic gradient counterparts and less computational complexity, as compared with other Newton-type algorithms.