We demonstrate that photoisomerizable liquid-crystal elastomer soft films can be used as tunable holographic gratings. Optomechanical mechanism of imprinting one-dimensional grating structure into the soft matrix by two-beam uv laser interference can be clearly resolved from the time dependence of the reading beam diffraction patterns. We analyze the observed response in terms of cis-trans isomerization-controlled modulation of the grating profile. The grating period can be tuned reversibly by stretching or contraction of the specimen, either thermomechanically or by applying external stress. Temperature-induced modifications of the grating parameters in the vicinity of the nematic-paranematic phase transition are also examined.