Detecting single photon level signals--carriers of both classical and quantum information--is particularly challenging for low-energy microwave frequency excitations. Here we introduce a superconducting amplifier based on a Josephson junction transmission line. Unlike current standing-wave parametric amplifiers, this traveling wave architecture robustly achieves high gain over a bandwidth of several gigahertz with sufficient dynamic range to read out 20 superconducting qubits. To achieve this performance, we introduce a sub-wavelength resonant phase matching technique that enables the creation of nonlinear microwave devices with unique dispersion relations. We benchmark the amplifier with weak measurements, obtaining a high quantum efficiency of 75% (70% including following amplifier noise). With a flexible design based on compact lumped elements, this Josephson amplifier has broad applicability to microwave metrology and quantum optics.