Moisten the adhesive side of the wallpaper that is peeling away from the wall using a sponge that is wet but not dripping. This prepares the wallpaper so that it will more easily bond with additional wallpaper glue.
Pull back the wallpaper slightly, being careful not to tear it in the process. Apply a thin layer of wallpaper glue using a small paintbrush. The glue can be applied to the wall beneath the paper or to the underside of the paper itself, but not to both since that may cause excess glue buildup or problems with the glue drying properly.
Press the wallpaper back against the wall. Squeeze some of the water out of your sponge so that it is merely damp, then brush across the wallpaper to moisten it slightly and aid it in bonding. Move the sponge from the center of the wallpaper toward the seam, going over the entire area where you applied new glue.
Check the wallpaper after the glue has dried to make sure that the repair fixed the peeling. If other sections of the wallpaper are still peeling, repeat the process to apply more glue as needed.