Recent experiments indicate that the calcium store (e.g., endoplasmic reticulum) is involved in electrical bursting and [Ca2+]i oscillation in bursting neuronal cells. In this paper, we formulate a mathematical model for bursting neurons, which includes Ca2+ in the intracellular Ca2+ stores and a voltage-independent calcium channel (VICC). This VICC is activated by a depletion of Ca2+ concentration in the store, [Ca2+]CS. In this model, [Ca2+]CS oscillates slowly, and this slow dynamic in turn gives rise to electrical bursting. The newly formulated model thus is radically different from existing models of bursting excitable cells, whose mechanism owes its origin to the ion channels in the plasma membrane and the [Ca2+]i dynamics. In addition, this model is capable of providing answers to some puzzling phenomena, which the previous models could not (e.g., why cAMP, glucagon, and caffeine have ability to change the burst periodicity). Using mag-fura-2 fluorescent dyes, it would be interesting to verify the prediction of the model that (1) [Ca2+]CS oscillates in bursting neurons such as Aplysia neuron and (2) the neurotransmitters and hormones that affect the adenylate cyclase pathway can influence this oscillation.