In order to introduce the burst firing, a nerve-cell dynamic feature, we extend the Inverse function Delayed model (ID model), which is the neuron model with ability to oscillate and has powerful ability on the information processing. This dynamics is discussed for the relation with the functional role of the brain and is characterized by repeated patterns of closely spaced action potentials. It is expected that the additional new characteristics add extra functions to neural networks. Using the relation between the ID model and reduced Hodgkin-Huxley model, we propose the neuron model with ability of burst. The proposed model excelled the ID model in solving the N-Queen problem. Additionally, the prototype chip for the burst ID model is implemented and measured.