The validity of the mono or multi-fluid descriptions and the determination of closure approximations in a magnetized collisionless plasma are important issues for the simulation of realistic three-dimensional problems for which the integration of the Vlasov-Maxwell system is still impossible. We present a mono-fluid model with Landau damping, specifically adapted for the description of MHD waves in a collisionless plasma permeated by a strong ambient magnetic field where the distribution functions are close to bi-Maxwellians. This model that can be viewed as an extension of the Landau-fluid model of Snyder, Hammett and Dorland (1997), is able to describe oblique or kinetic Alfv´en waves for which the Hall effect as well as finite Larmor radius corrections are relevant. It includes dynamical equations for the gyrotropic components of the pressure and heat flux tensors. The latter equations that contain non local operators associated with wave-particle resonances are built in a way that reproduces the weakly nonlinear dynamics of Alfv´en and magnetosonic waves with a wavelength long compared to the ion Larmor radius, whatever the propagation direction. This model will be particularly useful to study the formation of coherent structures such as magnetic holes or shocklets and also to perform three-dimensional numerical simulations of dispersive MHD turbulence taking into account realistic dissipation and heating mechanisms. Further applications include the interpretation of spectra and structures observed in the solar wind and the terrestrial magnetosheath.