The concept we recently introduced of a coronagraph using a four-quadrant phase mask has been the subject of detailed model calculations and of laboratory validation proving its great potential in planet finding. A nulling factor of 12500 is already demonstrated in the laboratory (Riaud et al., this conference). We first remind the principle of the 4QC: a destructive interference between the two equal fractions of the amplitude with opposite signs produces a very efficient nulling of the_star light. We propose to install such a device on several ground-based and space instruments, including present (NAOS/CONICA) or future (Planet Finder) VLT instruments and MIRI, the mid-IR camera of the NGST. The present paper focus on the question of direct imaging of exoplanets using this type of device. Indeed, one advantage of the four-quadrant coronagraph is to permit probing the vicinity of a star down to smaller angular distances than a classical Lyot mask. We examine the sources of uncertainties in different cases of optimized ground-based and space experiments and different situations of planet/star couples, using as far as possible realistic models of planetary evolution. On the VLT, even with an extremely powerful adaptive optics system, the speckle noise will be the main limitation: contrast in magnitude as large as Dm = 15 are however possible in the K band. The combination of a 4QC and differential imaging at two wavelength is likely the most promising concept for direct planet Detection from the ground. On the other hand, we show that with a 4QC on MIRI, a classical Jupiter is indeed detectable from space and at 20 μm for a star closer than 10 pc, while the more favorable cases of a young (hot) giant planet allows detection at 6 μm for a star belonging to the closest star forming region at 50 pc.