Enhancing environmental sustainability in maritime shipping has emerged as an important topic for both firms in shipping-related industries and policy makers. Speed optimization has been proven to be one of the most effective operational measures to achieve this goal, as fuel consumption and greenhouse gas (GHG) emissions of a ship are very sensitive to its sailing speed. Existing research on ship speed optimization does not differentiate speed through water (STW) from speed over ground (SOG) when formulating the fuel consumption function and the sailing time function. Aiming to fill this research gap, we propose a speed optimization model for a fixed ship route to minimize the total fuel consumption over the whole voyage, in which the influence of ocean currents is taken into account. As the difference between STW and SOG is mainly due to ocean currents, the proposed model is capable of distinguishing STW from SOG. Thus, in the proposed model, the ship's fuel consumption and sailing time can be determined with the correct speed. A case study on a real voyage for an oil products tanker shows that: (a) the average relative error between the estimated SOG and the measured SOG can be reduced from 4.75% to 1.36% across sailing segments, if the influence of ocean currents is taken into account, and (b) the proposed model can enable the selected oil products tanker to save 2.20% of bunker fuel and reduce 26.12 MT of CO2 emissions for a 280-h voyage. The proposed model can be used as a practical and robust decision support tool for voyage planners/managers to reduce the fuel consumption and GHG emissions of a ship.