Nonorthogonal coded agreements and decoy state method can effectively protect the photon number against splitting attack. Owing to the fact that the component of single-photon in the coherent-state superposition (CSS) is as high as 90%, CSS has recently emerged as an alternative to single-photon qubits for quantum information processing and metrology. The approximate CSS of small amplitudes is generated by the subtraction of photons from a squeezed vacuum state, and the approximate CSS of large amplitude is generated from Fock state by using a single homodyne detection. Here, we combine both of the methods and propose a new protocol by using the CSS as a light source. We derive the secure key generation rate, the lower bound of count rate and upper bound of error rate of single-photon. We simulate the curves relationship between secure key generation rate and safety transmission distance in the case of an infinite number of decoy states by using matlab. The parameters are given according to the Gobby-Yuan-Shields (GYS) experiment. We infer that the safety transmission distance achieves 147.4 km and the secure key generation rate is much higher than those of other schemes. We also simulate the relationship between key generation rate and safety transmission distance in the case of a limited number of decoy states by using matlab. The parameters are given according to the GYS experiment too. When the N is 1010, the safety transmission distance achieves 144 km; when the N is 109, the safety transmission distance achieves 139 km; when the N is 108, the safety transmission distance achieves 125.9 km. In this paper, we propose the use of CSS as the light source. Combining SARG04 agreements and decoy state, the scheme has the following advantages: first, the scheme which combines SARG04 agreements and decoy state method can effectively resist PNS; second, nonorthogonal decoy-state quantum key distribution based on coherent-state superpositions has a longer safety transmission distance and higher secure key generation rate than nonorthogonal decoy-state quantum key distribution based on weak coherent pulse and nonorthogonal decoy-state quantum key distribution based on conditionally prepared down-conversion source; third, nonorthogonal decoy-state quantum key distribution based on coherent-state superpositions is easier to prepare, which just needs one decoy state, than other schemes that require several decoy states. Obviously, our scheme can enhance the performance of quantum key distribution. Nonorthogonal decoy-state quantum key distribution based on coherent-state superpositions will have a very good application with the further development of preparation technology of CSS.