Despite the prevalence of synchronization analysis on complex dynamical networks, little attention was paid to the problem of estimating their regions of attraction. This paper addresses the issue of estimating the region of attraction of an equilibrium point of a complex dynamical network, and briefly analyzes the network stability. A sufficient condition and a necessary condition are first established for the asymptotical stability of the network equilibrium point. Then, a general technique for region-of-attraction estimation is developed by combining the network structure and the node dynamics. In order to avoid the troublesome parameter selection in general region-of-attraction estimation, second-order estimation is solved under a mild additional condition. Examples are provided to verify the theoretical estimations.