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 determining 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, particularly 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 of Ji et. al, is used in order to relax the fluid approximation and propose a general moment hierarchy. A separation between parallel and perpendicular moments is performed, allowing the inclusion of kinetic effects in the parallel dynamics, even in the presence of finite collisionality. The resulting model is analysed in the fluid and kinetic limits, comparing with known models, such as the drift-reduced Braginskii equations.