Optical scanning holography (OSH) is a promising technique to acquire a big-size digital hologram. However, the acquisition speed is limited by the mechanical scanner. In this Letter we apply the OSH in conjunction with an anisotropic low-pass filtering pupil to acquire vertical-bandwidth-limited (VBL) holograms. The size and the acquisition time of the VBL hologram can be reduced by one order of magnitude while the horizontal resolution remains the same as the conventional scanning hologram. The VBL hologram can be coded as an off-axis hologram without any postfiltering. Meanwhile, the full horizontal bandwidth of the displaying device can be capitalized.