We report the discovery of a planet - OGLE-2014-BLG-0676Lb- via gravitational microlensing. Observations for the lensing event were made by the following groups: Microlensing Observations in Astrophysics; Optical Gravitational Lensing Experiment; Wise Observatory; RoboNET/Las Cumbres Observatory Global Telescope; Microlensing Network for the Detection of Small Terrestrial Exoplanets; and μ-FUN. All analyses of the light-curve data favour a lens system comprising a planetary mass orbiting a host star. The most-favoured binary lens model has a mass ratio between the two lens masses of (4.78 ± 0.13) × 10-3. Subject to some important assumptions, a Bayesian probability density analysis suggests the lens system comprises a 3.09 +1.02 -1.12 MJ planet orbiting a 0.62 +0.20 -0.22 M⊙ host star at a deprojected orbital separation of 4.40 +2.16 -1.46 au. The distance to the lens system is 2.22 +0.96 -0.83 kpc. Planet OGLE-2014-BLG-0676Lb provides additional data to the growing number of cool planets discovered using gravitational microlensing against which planetary formation theories may be tested. Most of the light in the baseline of this event is expected to come from the lens and thus high-resolution imaging observations could confirm our planetary model interpretation.