Computer simulation of a magnetohydrodynamic (MHD) dynamo is performed. A magnetic field is generated by the thermal convection motion of an electrically conducting fluid in a rotating spherical shell. This study is motivated by the mysterious origin of the earth's dipole field. It is shown that a strong dipole field is spontaneously generated by the MHD dynamo. The dipole field generation is closely related to the columnar structure of the convection motion, which is characteristic of the rotating spherical convection.