Owing to its high carrier mobility and saturation velocity, graphene has attracted enormous attention in recent years. In particular, high-performance graphene transistors for radio-frequency (r.f.) applications are of great interest. Synthesis of large-scale graphene sheets of high quality and at low cost has been demonstrated using chemical vapour deposition (CVD) methods. However, very few studies have been performed on the scaling behaviour of transistors made from CVD graphene for r.f. applications, which hold great potential for commercialization. Here we report the systematic study of top-gated CVD-graphene r.f. transistors with gate lengths scaled down to 40 nm, the shortest gate length demonstrated on graphene r.f. devices. The CVD graphene was grown on copper film and transferred to a wafer of diamond-like carbon. Cut-off frequencies as high as 155 GHz have been obtained for the 40-nm transistors, and the cut-off frequency was found to scale as 1/(gate length). Furthermore, we studied graphene r.f. transistors at cryogenic temperatures. Unlike conventional semiconductor devices where low-temperature performance is hampered by carrier freeze-out effects, the r.f. performance of our graphene devices exhibits little temperature dependence down to 4.3 K, providing a much larger operation window than is available for conventional devices.