We present an alteative scheme to exactly implement one-qubit and two-qubit quantum gates with a single trapped cold ion driven by a travelling laser field. The inteal degree of freedom of the ion acts as the target qubit and the control qubit is encoded by two Fock states of the exteal vibration of the ion. The conditions to realize these operations, including the duration of each applied laser pulse and Lamb-Dicke parameter, are derived. In our scheme neither the auxiliary atomic level nor the Lamb-Dicke approximation is required. The multiquantum transition between the inteal and exteal degrees of freedom of the ion is considered.