We theoretically investigate single-photon scattering and nonreciprocal transmission in a coupled resonator waveguide which is coupled to a driven three-level giant atom via two distant sites. In our system, the local coupling phases are introduced to induce intriguing interference effects. As a result, the phase difference can serve as a sensitive controller for the photon scattering. It is found that the photon scattering properties can be effectively tailored by the size of the giant atom, the driving field and the phase difference. Intriguingly, by carefully tuning the parameters such as the atomic dissipation and the phase difference, a perfect nonreciprocal single-photon transmission can be realized. Additionally, the photon frequency can be adjusted by modulating Rabi frequency of the driving field. These results have significant potential for the development of nonreciprocal optical devices using the giant-atom configuration.