We report in this work that quantum efficiency can be significantly enhanced in an ultra-thin silicon solar cell coated by a fractal-like pattern of silver nano cuboids. When sunlight shines this solar cell, multiple antireflection bands are achieved mainly due to the self-similarity in the fractal-like structure. Actually, several kinds of optical modes exist in the structure. One is cavity modes, which come from Fabry-Perot resonances at the longitudinal and transverse cavities, respectively; the other is surface plasmon (SP) modes, which propagate along the silicon-silver interface. Due to the fact that several feature sizes distribute in a fractal-like structure, both low-index and high-index SP modes are simultaneously excited. As a whole effect, broadband absorption is achieved in this solar cell. Further by considering the ideal process that the lifetime of carriers is infinite and the recombination loss is ignored, we demonstrate that external quantum efficiency of the solar cell under this ideal condition is significantly enhanced. This theoretical finding contributes to high-performance plasmonic solar cells and can be applied to designing miniaturized compact photovoltaic devices.