Thin hydrogel films attached to a rigid substrate can only swell along the direction perpendicular to the substrate, which generates compressive stress within the gel. When the stress is sufficiently large, the free surface of the gel will locally buckle and fold against itself to form various wrinkling patterns. Here we show that hydrogen-bonded layer-by-layer (LBL) films of poly(vinyl pyrrolidone) (PVPON) and poly(acrylic acid) (PAA) also swell in ethanol/water mixtures. Like ordinary hydrogel films attached to a substrate, the LBL films also undergo mechanical instability when their swelling degree is large enough. By adjusting the composition and pH of the ethanol/water mixture, the swelling degree of the film can be adjusted, which further decides whether the mechanical instability occurs or not. Like ordinary hydrogel films, the surface wrinkling of the PVPON/PAA films occurs via a nucleation-growth process. Unlike ordinary hydrogels, the critical swelling degree for the onset of wrinkling for PVPON/PAA films increases with increasing film thickness. More importantly, the wrinkling patterns can be healed automatically, because the transient network of PVPON/PAA films allows for the relief of compressive stress via its rearrangement. The phenomenon observed here may provide a possible way to erase the undesired wrinkling patterns on constrained hydrogel films.