A strong axial magnetic dipole field with magnetic energy 15 times larger than the kinetic energy of thermal convection is realized by a direct numerical simulation of the magnetohydrodynamic equation of an electrically conducting Boussinesq fluid in a rotating spherical shell which is driven by a temperature difference between the outer and inner boundaries against a gravity force pointed towards the system centre. Cyclonic and anticyclonic convection vortices are generated and play a primary role in the magnetic field intensification. The magnetic field is enhanced through the stretching of magnetic lines in four particular parts of the convection fields, namely inside anticyclones, between cyclones and their western neighbouring anticyclones at middle as well as low latitudes, and between anticyclones and the outer boundary. A ‘twist-turn’ loop of intense magnetic flux density is identified as a fundamental structure which yields dominant contributions both to the toroidal and poloidal components of the longitudinally averaged magnetic field. Various types of competitive interaction between the magnetic field and convection vortices are observed. Among these, a creation-and-annihilation cycle in a statistically equilibrium state is particularly important. It is composed of three sequentially recurrent dynamical processes: the generation of convection vortices by the Rayleigh–Bénard instability, the growth of anticyclones and the intensification of magnetic field by a concentrate-and-stretch mechanism, and the breakdown of vortices by the Lorentz force followed by diminution of the magnetic field. The energy transfer from the velocity to the magnetic fields takes place predominantly in this dynamical cycle.