Since the first observation of criticality in neural systems, many researchers have thought that the nervous system can operate in a critical state, and an increasing number of models equipped with different mechanisms have been proposed. We believe that there are simple mechanisms underlying the criticality in neural systems. We constructed a neural network model to investigate the mechanism underlying criticality in neural systems. We found that a neural system consisting of neurons with all-or-none dynamics and local-range dominated interaction exhibits critical behavior when properly driven. The all-or-none dynamics of single neuron and local-range dominated interaction are the identical mechanisms of criticality in the BTW sandpile model, so we concluded that whatever mechanism causes the neural system to evolve to the state where short-range dominated interaction and appropriate input is received, critical behavior can be observed.