Memristor is a nanoscale device which consumes low power and shows good compatibility with CMOS circuits. It has applications in memory circuits, logic circuits as well as in neuromorphic systems to imitate biological synapses. The use of this device to implement neuron models can improve the scalability of neuromorphic circuits. In this paper a Leaky Integrate and Fire model of neuron is presented by a memristor-CMOS hybrid circuit which requires 16 MOSFETs, 1 memristor and 1 capacitor. The model has been applied in a simple configuration of one neuron driving another. Additionally, it has been used in an associative learning circuit to exhibit functionality. Such successful incorporation of the proposed design in learning networks founds the ground of further expansion and implementation of larger networks using neuron circuits.