During rest, the human brain performs essential functions such as memory maintenance, which are associated with resting-state brain networks (RSNs) including the default-mode network (DMN) and frontoparietal network (FPN). Previous studies based on spiking-neuron network models and their reduced models, as well as those based on imaging data, suggest that resting-state network activity can be captured as attractor dynamics, i.e., dynamics of the brain state toward an attractive state and transitions between different attractors. Here, we analyze the energy landscapes of the RSNs by applying the maximum entropy model, or equivalently the Ising spin model, to human RSN data. We use the previously estimated parameter values to define the energy landscape, and the disconnectivity graph method to estimate the number of local energy minima (equivalent to attractors in attractor dynamics), the basin size, and hierarchical relationships among the different local minima. In both of the DMN and FPN, low-energy local minima tended to have large basins. A majority of the network states belonged to a basin of one of a few local minima. Therefore, a small number of local minima constituted the backbone of each RSN. In the DMN, the energy landscape consisted of two groups of low-energy local minima that are separated by a relatively high energy barrier. Within each group, the activity patterns of the local minima were similar, and different minima were connected by relatively low energy barriers. In the FPN, all dominant local minima were separated by relatively low energy barriers such that they formed a single coarse-grained global minimum. Our results indicate that multistable attractor dynamics may underlie the DMN, but not the FPN, and assist memory maintenance with different memory states.