In nonlinear and chaotic time series prediction, constructing the mathematical model of the system dynamics is not an easy task. Partially connected Artificial Neural Network with Evolvable Topology (PANNET) is a new paradigm for prediction of chaotic time series without access to the dynamics and essential memory depth of the system. Evolvable topology of the PANNET provides flexibility in recognition of systems in contrast to fixed layered topology of the traditional ANNs. This evolvable topology guides the relationship between observation nodes and hidden nodes, where hidden nodes are extra nodes that play the role of memory or internal states of the system. In the proposed variable-length Genetic Algorithm (GA), internal neurons can be connected arbitrarily to any type of nodes. Besides, number of neurons, inputs and outputs for each neuron, origin and weight of each connection evolve in order to find the best configuration of the network.