In this work a Smoothed Particle Hydrodynamics model is presented to study rheology and microstructure of a non-colloidal suspension of spherical particles in a Newtonian solvent. The scheme presented in (Bian and Ellero, 2014) is extended to three-dimensions incorporating both normal and tangential short-range interparticle lubrication forces which are solved implicitly with a refined splitting strategy. The scheme allows to bypass prohibitively small time steps generally required for handling divergent lubrication forces and allows to simulate large particle systems. Rheology of a three-dimensional hard-spheres suspension confined in a plane Couette rheometer is investigated for concentrations up to phi = 0.5. Results for the relative suspension viscosity eta(r), are analyzed against sample size and numerical convergence of the splitting lubrication scheme and compared with available experimental and simulations data. Very close agreement with the experiments is obtained for eta(r) up to phi = 0.35. At larger concentrations, our results are still unable to explain the significant viscosity increase observed in experiments. Modest shear-thickening is also observed which is related to anisotropy of the particle radial distribution function (RDF) and presence of reversible hydrodynamic aggregates increasing in size with increasingly applied shear rates. (C) 2015 Elsevier B.V. All rights reserved.