A sufficient and necessary condition for the breakdown of gas gap for Townsend discharge is defined based on experimental results. Furthermore, a new breakdown criterion for Townsend discharge is presented based on the theory of gas discharge and the continuity equations for electrons and positive ions. The presented breakdown criterion overcomes the limitation of the Townsend breakdown criterion (which demands that the discharge current tends towards infinity) and agrees well with actual situation while meeting the current continuity theorem. These results provide a new way of thinking to understand the essence of gas breakdown for Townsend discharge.