This paper introduces a symbiotic neuron evolution algorithm (SNEA) to determine the topology of a neural-network-aided grey model (NNAGM) for time series prediction problem. The SNEA uses an evolutionary approach to evolve partially connected neural networks (NNs) and determine the number of hidden neurons. To achieve symbiotic evolution, SNEA first establishes a neuron population where each neuron is randomly created, and evaluates the neurons by constructing NNs with different numbers of neurons. Each neuron shares fitness from participating NNs. This algorithm then performs evolution on the neuron population by crossover and mutation based on neuron fitness. An NNAGM designed by SNEA is applied to the prediction problems and compared with other methods. The experimental results show that SNEA can produce an NNAGM with appropriate topology and higher prediction performance than other methods.