Achieving multiple diversified functionalities in a single flat device is crucial for electromagnetic (EM) integration, but available efforts suffer the issues of device thickness, low-efficiency and restricted functionalities. Here we describe a general strategy to design high-efficiency bifunctional devices based on meta-surfaces composed by anisotropic meta-atoms with polarization-dependent phase responses. Based on the derived general criterions, we design and fabricate two bifunctional meta-devices, working in reflection and transmission modes, respectively, that can realize two distinct functionalities with very high efficiencies (~90% in reflection geometry and ~72% in transmission one). Microwave experiments, including both far-field and near-field characterizations, are performed to demonstrate the predicted effects, which are in excellent agreement with numerical simulations. Our findings can motivate the realizations of high-performance bifunctional meta-devices in other frequency domains and with different functionalities, which are of crucial importance in EM integration.