Functional integration is crucial and has become a research interest in recent years; however, available efforts suffer from low efficiency and narrow operating bandwidth. Here, we propose a novel strategy to design bifunctional meta-surface with high efficiency and largely enhanced bandwidth in reflection geometry. For demonstration, we designed and fabricated a bifunctional meta-surface which enables both focusing and anomalous reflection under different polarizations. The working bandwidth is significantly extended by using the dual-resonant three-turn meander-line resonator (TMLR) element which provides an almost consistent phase response within a large frequency interval. For potential applications, we engineered a bifunctional antenna by launching the designed meta-surface with proper feed sources. Numerical and experimental results coincide well, indicating bifunctionalities of high gain pencil-beam radiation (reflectarray) and beam steering radiation with comparable performances. Our results can stimulate the realizations of high-performance meta-surfaces and antenna systems.