A fluid drift-reduced description, which accurately describes phenomena occurring on time scales slower than the characteristic gyro-frequencies and space scales longer than the Larmor radii, has been successfully used in recent years to model the dynamics of tokamak scrape-off layer (SOL). This region controls the tokamak power and particle exhaust and plays an important role in de- termining the overall plasma confinement of this device, an issue of utmost importance in the fusion program. The fluid model assumed in the drift-reduced plasma description relies on the typical length scales being longer than the characteristic mean free path. This is not true in general, particu- larly during edge-localised modes in H-mode plasmas. The goal of the present work is to introduce a drift-kinetic model for SOL plasmas that overcomes the limitations of fluid models. As in the SOL the magnitude of equilibrium and perturbation fields may be of the same order, a full-f model is employed with the full Coulomb collision operator. The Coulomb moment expansion is used in order to relax the fluid approximation and pro- pose a general moment hierarchy. A separation between parallel and perpendicular moments is per- formed, allowing the inclusion of kinetic effects in the parallel dynamics, even in the presence of fi- nite collisionality. The resulting model is analysed in the fluid and kinetic limits, comparing with known models, such as the drift-reduced Braginskii equations.