The security of quantum-key-distribution system is analyzed using the decoy state protocol with two weak decoy states and one signal state. The comparison is based on the key generation rate as a function of distance for two types of decoy states: the vacuum and a weak decoy state, asymptotically approaching the theoretical limit of the most general type of decoy protocol, one-decoy-state protocol. We studied the two-decoy-state protocol in connection with the intensity of signal state, and the gain of signal states, the overall quantum bit error rate, the gain of single-photon states and the error rate of single-photon states and arrived at the optimal condition which maximizes the key generation rate.