To enhance the core heating efficiency in fast ignition laser fusion, the concept of relativistic electron beam guiding by external magnetic fields was evaluated by integrated simulations for FIREX class targets. For the cone-attached shell target case, the core heating performance is deteriorated by applying magnetic fields since the core is considerably deformed and the most of the fast electrons are reflected due to the magnetic mirror formed through the implosion. On the other hand, in the case of cone-attached solid ball target, the implosion is more stable under the kilo-tesla-class magnetic field. In addition, feasible magnetic field configuration is formed through the implosion. As the results, the core heating efficiency becomes double by magnetic guiding. The dependence of core heating properties on the heating pulse shot timing was also investigated for the solid ball target.T. Johzaki, et al., "Integrated simulation of magnetic-field-assist fast ignition laser fusion" Prepared for submission to Plasma Phys. Control. Fusion (43rd EPS Conference on Plasma Physics)