The present study deals with the interaction between the magnetic field of Jupiter and ones of the Coronal Mass Ejections (CMEs) for three years (2011-2013) which includes the peak of Solar cycle 24. These interactions were studied through numerical simulation using Magneto hydrodynamic models (MHD) and solved numerically by Leapfrog method with the aid of MATLAB program. The data related to CMEs were derived from LASCO/SOHO, and were verified whether there are events or not by checking them from ERNE detectors (LASCO and ERNE are scientific systems on board SOHO). While the data which concern with Jupiter were taken from VOYAGER 1. The simulation were achieved in two stages; firstly, the beginning simulation of the lunched CMEs from the surface of the Sun until they reach behind the boundary of the magnetosphere of Jupiter through interplanetary using the ideal MHD model (conservative model), and secondly is being the simulation of the interaction between the magnetic field of the CMEs and ones of Jupiter. It is verified using Semi-relativistic MHD model. Accordingly, it was found that Leapfrog numerical analysis is the optimal and best method. In addition, the outgoing CMEs to Jupiter embraces impulsive type and associated with Flares. Furthermore, it has been noted from the numerical simulation that intensity of the final magnetic field after the interaction of CMEs magnetic field with Jupiter magnetic field is going to increase giving rise to positive correlation with the speed of the adopted CMEs. On the other hand, the fast MHD shock wave with convex surface was created, because the speed of the adopted CMEs were greater than Alfven speed.