Although the wide integration of advanced metering infrastructure on distribution network facilitates the application of volt/var optimisation (VVO) in real-time circumstance, the contradiction between heavy computation load and low solution efficiency is still a big challenge, thus the system scales investigated in the literature are limited. In this study, the full AC real-time VVO is formulated based on particle swarm optimisation (PSO) framework and direct approach (DA) power flow method, where all components, such as distributed generator and on-load tap changer transformer, are formulated and integrated into the iterative DA process. Since both PSO and DA are suitable for parallel implementation, the graphics processing unit (GPU) is introduced for acceleration in order to achieve the possibility for real-time application. All the solution process is executed by GPU with the well-established data structure and thread organisation pattern, resulting in high efficiency by guaranteeing coalesced access within each warp. Case studies are conducted on four systems with sizes ranging from 136-bus to 1760-bus. Solution accuracy and convergence property are validated by the popular open source package Matpower. Based on the results from solution efficiency comparison between CPU sequential, CPU parallel, and GPU parallel programs, the promise of the proposed parallel implementation scheme for practical application is established.