This peper proposes a simplified model of the well-known two-neuron neural oscillator. By eliminating one of the two positive feedback synapses in the neural oscillator, learning for the in-phase control of the oscillator is shown to be achievable via a very simple learning rule. The learning rule is devised in such a way that only the plasticity of two synaptic weights are required. We demonstrate some examples of the synchronization learning to validate the efficiency of the learning rule, and finally by illustrating the dynamics of the synchronization learning and by using computer simulation, we show the convergence behavior and the stability of the learning rule for the two-neuron simple neural oscillator.