A Personal Sound Zones (PSZ) system aims to generate two or more independent listening zones that allow multiple users to listen to different music/audio content in a shared space without the need for wearing headphones. Most existing studies assume that the acoustic paths between loudspeakers and microphones are measured beforehand in a stationary environment. Recently, adaptive PSZ systems have been explored to adapt the system in a time-varying acoustic environment. However, because a PSZ system usually requires multiple loudspeakers, the multichannel adaptive algorithms impose a high computational load on the processor. To overcome that problem, this paper proposes an efficient distributed algorithm for PSZ systems, which not only spreads the computational burden over multiple nodes but also reduces the overall computational complexity, at the expense of a slight decrease in performance. Simulation results with true room impulse responses measured in a Hemi-Anechoic chamber are performed to verify the proposed distributed PSZ system.