The modulator is a key component in optical communications. Several graphene-based amplitude modulators have been reported based on electro-absorption. However, graphene phase modulators (GPMs) are necessary for functions such as applying complex modulation formats or making switches or phased arrays. Here, we present a 10 Gb s–1 GPM integrated in a Mach–Zehnder interferometer configuration. This is a compact device based on a graphene-insulator–silicon capacitor, with a phase-shifter length of 300 μm and extinction ratio of 35 dB. The GPM has a modulation efficiency of 0.28 V cm at 1,550 nm. It has 5 GHz electro-optical bandwidth and operates at 10 Gb s–1 with 2 V peak-to-peak driving voltage in a push–pull configuration for binary transmission of a non-return-to-zero data stream over 50 km of single-mode fibre. This device is the key building block for graphene-based integrated photonics, enabling compact and energy-efficient hybrid graphene–silicon modulators for telecom, datacom and other applications.