The influence of long-range links on spiral waves in an excitable medium has been investigated.Spatiotemporal dynamics in an excitable small-world network transform remarkably when we increase the long-range connection probability P.Spiral waves with few perturbations,broken spiral waves,pseudo spiral turbulence,synchronous oscillations,and homogeneous rest state are discovered under different network structures.Tip number is selected to detect non-equilibrium phase transition between different spatiotemporal pattes.The Kuramoto order parameter is used to identify these pattes and explain the emergence of the rest state.Finally,we use long-range links to successfully control spiral waves and spiral turbulence.