The compression of an external magnetic field by a laser-driven implosion is studied by using the two-dimensional resistive magneto-radiation hydrodynamic simulation code for electron-beam guiding in fast ignition. The simulation results show that it is possible to compress the magnetic field to 1 kT (107 G); however, the strong magnetic field affects the implosion dynamics because of the suppression of the electron heat flux that crosses the strong magnetic field lines. This result suggests that care must be taken to design a target and the initial conditions for fast ignition with an external magnetic field not only to control the hot electron transport but also to form the high-density plasma.