Graphene electro-optic modulators (GEOMs) are emerging as a viable alternative to conventional material-based modulators mainly due to their broadband and ultrafast performance. These GEOMs with combined advantages of small footprint and low energy consumption can potentially enable various high-performance applications that are not possible using conventional approaches. Here, we report the first actively Q-switched lasers with a GEOM. In contrast to the previously reported lasers that are passively modulated by two-dimensional layered material-based saturable absorbers, our actively modulated laser concept represents significant advantages, such as electrically tunable output parameters (e.g. output repetition rate, pulse duration and pulse energy) and electro-optical synchronization. Using a single GEOM, we generate broadband Q-switched pulses at 1.55 and 2μm with output energies of up to 123 nJ. This indicates the broadband pulse generation capability of the graphene-based active devices, superior to widely used bulk material-based active modulation approaches. Our results demonstrate a simple and viable design towards broadband, high-repetition-rate, electrically modulated ultrafast lasers for various applications, such as telecommunications and spectroscopy.