In this paper we present an adaptive block-based eigenvector algorithm (BBEVA) for blind equalization of time-varying multipath fading channels. In addition we assess the performance of the new algorithm for different configurations and compare the results with the least mean squares (LMS) algorithm. The new algorithm is evaluated in terms of intersymbol interference (ISI) suppression, mean squared error (MSE) and by examining the signal constellation at the output of the equalizer. Simulation results show that the BBEVA performs better than the non-blind LMS algorithm.