A novel constructing quantum fault-tolerant encoded gates method was proposed based on teleportation for the general stabilizer code. The quantum teleportation was used to get the teleported code and the imaginary encoded gate was applied to the teleported code, then move it forward, so the difficulty to construct encoded gate can be reduced to prepare a special ancillary state. The encoded Hadamard gate and phase gate were selected as examples to explain the constructing procedure, and the numerical analysis verifies that the method is valid. The results show that under the teleportation method, encoded H gate decreases 60n physical quantum gates, 5 encoded block |0> and 5 ancilla block |Cat>, and encoded P gate decreases 16n physical quantum gates, 1 encoded block |0> and 2 ancilla block |Cat> when compared with the overhead in reference ［16］.