By researching the ternary counter and low power circuit design method, a novel design of low power ternary Domino counter on switch-level is proposed. Firstly, the switch-level structure expression of ternary loop operation circuit with enable pin is derived according to the switch-signal theory, and the one bit ternary counter is obtained combining the ternary adiabatic Domino literal operation circuit and buffer. Then the switch-level structure expression of enable signal circuit is derived, and the four bits ternary counter is obtained by cascade connection. Finally, the circuit is simulated by Spice tool and the output waveforms transform in proper order indicating that the logic function is correct. The energy consumption of the four bits ternary adiabatic Domino counter is 63% less than the conventional Domino counterpart.