A step-and-scan type scanning scheme has been investigated for the purpose of simplifying the high-precision scanning mechanism adopted in the 6.65-m off-plane Eagle type monochromator on an undulator beamline of the Advanced Light Source at Lawrence Berkeley National Laboratory. In this scheme it is proposed to scan over a wavelength range of 80-180 nm by covering a range of 0.99 lambda(t)-1.01 lambda(t) at a time by simply rotating the grating fixed at the position for a wavelength lambda(t) to which the undulator is tuned. When the undulator is tuned to another lambda(t), the grating is translated to a new fixed position and scanning is made by simple grating rotation. A ruled grating with varied line spacing and straight grooves and a holographic grating recorded with spherical wave-fronts were designed to match the proposed scanning scheme and to meet the required energy resolution of similar to 1.0 cm(-1) over the entire scanning range. The results of ray tracing show that the designed gratings with 2400 grooves/mm and 6.1-m radius of curvature would provide a resolution of less than or similar to 1 cm(-1), a good correction of astigmatism, and a grating travel distance of only 11 or 14 mm over the scanning range of 80-180 nm.