By analyzing the structure and principle of reversible counter and adiabatic domino circuit, a design scheme of ternary adiabatic domino reversible counter is proposed in this work. First, the ternary adiabatic domino circuit with reset port and set port is designed. And then, the positive and negative circulation circuit, carry and borrow circuit are designed respectively, such that the positive and negative counting and cascade of reversible counter are established. Based on the above design, the four bits ternary adiabatic domino reversible counter is achieved. HSPICE simulation results show that the designed circuit has the correct function and low power.