This paper presents a biologically inspired "integrate-and-fire (I&F) neuron" which has multiple input dendrites for adaptive weight storage. By using a capacitor-free integrator, longer time constant and smaller chip area can be achieved. A low-power Schmitt Trigger is used to implement the feedback loop to achieve smaller power consumption. Weights are stored by using floating gate MOS transistors as nonvolatile analog memory. Simulation results show that this I&F neuron can be utilized in an analog VLSI neural network system.