We performed 2.5 dimensional numerical simulations of magnetized rotational core-collapse. From the observational fact, it is probable that gamma-ray bursts and core-collapse supernovae have same origin. And the very collimated jet is preferable to explain the light curve of their afterglow. How this collimated jet is produced due to the process of core-collapse of massive star? There are two main energy-sources for this explosion. One is neutrino pair annihilations and another is magneto-hydrodynamical process. In this time we concentrate the magneto-hydrodynamical process. We found a jet-like shock wave is launched in the direction of the pole. The strength of initial magnetic field determine the profile of jet. We found common structures of these jets. We continue the simulation that the jet-like shock wave produced at the center propagate to the surface of the star. Since the previous works are performed separately at each stage such as core-collapse and jet-propagation, many initial uncertainty remains in each stage. However we have performed the simulations from the magnetized core-collapse to the jet-propagation totally. This study gives us deeper knowledge on the relation between the profile of the jet and the progenitor.