A Simulink model of a spiking neural network of two neurons that works as a neural oscillator is presented. Each neuron is based upon Izhikevich Spiking Neuron Model. Average Response Model is used to model various aspects of synaptic transmissions. The parameters in the mathematical differential equation describing each neuron are set such that they exhibit a regular spiking pattern of cortical neurons. The duty cycle and frequency of oscillations of our oscillator are quite flexible and are tuned by varying one or more of a few parameters, for example, changing the nature of synapses. The presence of very few parameters reduces the complexity of simulation and allows this neural oscillator model to be easily implemented in myriad applications that involve sustained rhythmic patterns. An initial spike of stimulus is enough to drive this oscillator.