Noise that unavoidably exists in the quantum channel will distort transmitted information and destroy the communication. The superior scheme to overcome the noise at present is quantum error-avoiding code (QEAC). The quantum key distribution (QKD) using the QEAC will be robust in the quantum noisy channel without complex system. Six-photon error-avoiding code (SPEAC) is constituted and a robust QKD scheme based on it is proposed. In order to improve the qubit efficiency and the security of QKD, all the possible quantum states in the SPEAC are assembled, and as a result,an optimal scheme is developed,by which two key bits can be encoded in each state and Bob can decode the information successfully with an average probability of 7/16. Compared with the recent QKD scheme based on four-photon QEAC, the qubit efficiency of the authors' scheme increases by 16.67%, and the security is 3.5 times of it.