A round-robin differential-phase-shift quantum-key-distribution (QKD) protocol without three-photon pulses is proposed. This protocol can generate a secure key without monitoring signal disturbance, thus effectively reducing the complexity of implementation. Moreover, two kinds of intensity decoy states are applied to estimate the key rate in the proposed protocol. The results show that the key rate of the proposed protocol is significantly improved, and the corresponding maximum transmission distance is also increased. In addition, as only two-intensity decoy states are needed to achieve the same performance as infinite decoy states in the proposed protocol, the consumption of decoy states are effectively reduced.