The strong stiction of adjacent surfaces with meniscus is a major design concern in the devices with a micro-sized interface.Today, more and more research works are devoted to understand the adhesion mechanism. This paper concerns the elastic-plastic adhesion of a fractal rough surface contacting with a perfectly wetted rigid plane. The topography of rough surface is modeled with a two-variable Weierstrass-Mandelbrot fractal function. The Laplace pressure is dealt with the Dugdale approximation. Then the adhesion model of the plastically deformed asperities with meniscus can be established with the fractal microcontact model. According to the plastic flow criterion, the elastic-plastic adhesion model of the contacting rough surfaces with meniscus can be solved by combining the Maugis-Dugdale (MD) model and its extension with the Morrow method. The necessity for considering the asperities plastic deformation has been validated by comparing the simulation result of the presented model with that of the elastic adhesion model. The stiction mechanism of rough surfaces with meniscus is also discussed.