We present a lattice Boltzmann model designed for the simulation of dilute and dense finite-sized rigid particle suspensions under applied shear. We use a bottom-up approach and fully resolve the mechanical interaction between fluid and particles. Our model consists in coupling a lattice Boltzmann scheme for Newtonian and incompressible fluid flows with an immersed boundary scheme to simulate two-ways fluid-particles interaction. We introduce a simple yet robust contact model that includes repulsive elastic collision between particles, and neglects lubrication corrections. We apply this model to simple sheared flow with rigid spherical particles and we provide results for the relative apparent viscosity of the particle suspension as a function of the particle volume fraction and strain rate of the flow. We show that, using the proposed approach, there is no need for a lubrication model in the Newtonian regime, provided that an elastic contact model is included. Our algorithm, therefore, can be based only on physically sound and simple rules, a feature that we think to be fundamental for aiming at resolving polydispersed and arbitrarily shaped particle suspensions. Comparing our results with Krieger–Dougherty semi-empirical law, we confirm that the simulations are not sensitive to the particle Reynolds number for Rep ≪ 1 in the Newtonian regime. We show that the proposed model is sufficient to obtain a correct description of the rheology of particle suspension up to volume fraction equal to 0.55 (approaching the critical random packing fraction for monodispersed spheres), which goes beyond the state of the art.