Reservoirs of geological methane can occur within the sediments at any depth, right up to the seabed. Methane is also sequestered by gas hydrates. One mechanism to release methane from sediments to the ocean is through submarine mud volcanism, hydrocarbon seeps and vents. The 3D mathematical model of the dissolved gas transport by the ocean currents is used for the quantitative estimation of the scale of a possible methane flux into the atmosphere from the submarine fluid venting. The climatic large-scale currents field is obtained from the 3D global ocean dynamics model. The problem was numerically solved on a spatial grid with resolution of 3 degrees in latitude and in longitude with 24 levels on the vertical. In this case, a 3D equation of transport of dissolved methane from sources is simultaneously solved. Methane sources in this model are set taking into account a speed of a filtration methane flux. The calculated methane flux into the atmosphere exceeded 9-20 Tg/year, depending on the experiment scenario.