Complete control of the state of a quantum bit (qubit) is a fundamental requirement for any quantum information processing (QIP) system. In this context, all-optical control techniques offer the advantage of a well-localized and potentially ultrafast manipulation of individual qubits in multi-qubit systems. Recently, the negatively charged silicon vacancy centre (SiV-) in diamond has emerged as a novel promising system for QIP due to its superior spectral properties and advantageous electronic structure, offering an optically accessible Λ-type level system with large orbital splittings. Here, we report on all-optical resonant as well as Raman-based coherent control of a single SiV- using ultrafast pulses as short as 1 ps, significantly faster than the centre's phonon-limited ground state coherence time of about 40 ns. These measurements prove the accessibility of a complete set of single-qubit operations relying solely on optical fields and pave the way for high-speed QIP applications using SiV- centres.