An innovative solution to improve the performances of coronagraphs consists in adding, in the optical scheme, a dynamic hologram removing most of the residual speckle starlight. Our simulations show that the detection limit in the flux ratio between a host star and a very near planet, in the case of wavefront bumpiness imperfections at lambda/20 (resp. lambda/100), improves over a factor 1000 (resp. 10000) when equipped with a hologram, allowing to direct image an exo-Earth at a distance of 11 parsec with a 6.5m space telescope.