Quantum key distribution is proven to offer unconditional security in communication between two remote users with ideal source and detection. Unfortunately, ideal devices never exist in practice and device imperfections have become the targets of various attacks. By developing up-conversion single-photon detectors with high efficiency and low noise, we faithfully demonstrate the measurement-device-independent quantum-key-distribution protocol, which is immune to all hacking strategies on detection. Meanwhile, we employ the decoy-state method to defend attacks on a nonideal source. By assuming a trusted source scenario, our practical system, which generates more than a 25 kbit secure key over a 50 km fiber link, serves as a stepping stone in the quest for unconditionally secure communications with realistic devices.