Variable microwave-frequency couplers are highly useful components in classical communication systems, and likely will play an important role in quantum communication applications. Conventional semiconductor-based microwave couplers have been used with superconducting quantum circuits, enabling for example the in situ measurements of multiple devices via a common readout chain. However, the semiconducting elements are lossy, and furthermore dissipate energy when switched, making them unsuitable for cryogenic applications requiring rapid, repeated switching. Superconducting Josephson junction-based couplers can be designed for dissipation-free operation with fast switching and are easily integrated with superconducting quantum circuits. These enable on-chip, quantum-coherent routing of microwave photons, providing an appealing alternative to semiconductor switches. Here, we present and characterize a chip-based broadband microwave variable coupler, tunable over 4-8 GHz with over 1.5 GHz instantaneous bandwidth, based on the superconducting quantum interference device (SQUID) with two parallel Josephson junctions. The coupler is dissipation-free, features large on-off ratios in excess of 40 dB, and the coupling can be changed in about 10 ns. The simple design presented here can be readily integrated with superconducting qubit circuits, and can be easily generalized to realize a four- or more port device.