<p>Spiral waves exist in biological nervous systems and are associated with neurological diseases. In this paper, we propose an external periodic stimulation method to eliminate spiral waves in a neural network with local connections. Spiral waves can be generated spontaneously in the neural network. Under periodic boundary conditions, the generated spiral waves have only even spiral centers, whereas under open boundary conditions, the network can produce spiral waves with both even and odd spiral centers. Significant interhemispheric symmetry of spiral waves has been observed in the left and right hemispheres of the brain. Therefore, we focus primarily on eliminating spiral waves in neural networks with periodic boundary conditions. Regardless of whether the external periodic signal is a sinusoidal or square wave, a spiral wave can be eliminated if a signal with an appropriate amplitude and period is added to the network in the spiral wave state. After the external stimulus signal is withdrawn, the output of the network becomes a plane wave or synchronous oscillation under periodic boundary conditions, whereas the stable output is a target wave under open boundary conditions. The spiral-wave elimination method is simple and easy to implement, although its effectiveness in eliminating spiral waves depends on the amplitude and period of the stimulus signals.</p>