Gratings with low diffracted wavefront errors are crucial in many applications. Existing methods to reduce the diffracted wavefront errors of holographically produced gratings mainly address misalignment errors during exposure system adjustment, leaving the inevitable residual errors of collimation lenses uncorrected. The broad-beam scanning exposure method was recently proposed to fabricate gratings with large size and low stray light. We explore its ability to reduce the diffracted wavefront errors caused by both system misalignment and lens errors. During the exposure, the substrate translates in the direction perpendicular to the grating lines to pass through the exposure area, so the aberrations over different parts of the interference field along the scanning path are averaged. We prove the validity of this method by a theoretical analysis and numerical simulations. The averaging effect on different aberrations and with different scanning lengths is discussed. The peak-valley values of diffracted wavefront errors of gratings fabricated with an exposure field of defocus aberration and a more complicated aberration were reduced by 42.5% and 50%, respectively.