A new one-dimensional (1-D) parameterization of penetrative convection has been developed in order to have a better representation of the vertical mixing in ocean general circulation models. Our approach is inspired from atmospheric parameterizations of shallow convection which assumes that in the convective boundary layer, the subgrid-scale fluxes result from two different mixing scales: small eddies, which are represented by an Eddy-Diffusivity (ED) contribution, and large eddies associated with thermals, which are represented by a mass-flux contribution. In the present work, the local (small eddies) and nonlocal (large eddies) contributions are unified into an Eddy-Diffusivity-Mass-Flux (EDMF) parameterization which treats simultaneously the whole vertical mixing. EDMF is implemented in the community ocean model NEMO and tested in its 1-D column version. Deepening of dense water in analytic cases, successfully reproduced in LES simulations, is more realistic with EDMF than with standard diffusion parameterizations. Also the convective events observed in the western Mediterranean at the Lion station and in the North Pacific Ocean at the PAPA station are more realistic in terms of sequencing and amplitude with EDMF.