Marangoni flow created by the gradient of surface tension can be used to transport small objects along fluid interfaces. We study lateral motion of a fully wetted self-propelled body (swimmer) at a fluid-fluid interface. The swimmer releases a surfactant at a constant rate inducing a surface tension gradient. The dynamics of the insoluble surfactant is incorporated by taking into account advection by the Marangoni flow, surface diffusion and homogeneous decomposition reaction. We show that the translational speed of a Marangoni swimmer is increased as compared with the self-propulsion speed of a chemically inactive surface-bound swimmer. Flow induced in-plane rotation of the swimmer with an elongated body is generally weak so that its trajectory in the steady state is a straight line. A non-motile thin rod that releases surfactant at one of its ends is capable of surfing on the self-generated surfactant cloud. Steady surfing occurs along the body length with the source of the surfactant at the back end acting as a propulsion engine. © 2019 The Royal Society of Chemistry.