Assuming that the geomagnetic non-dipole field is created by the interaction between a strong toroidal magnetic field and convective motions, the velocity field in the earth's core is estimated. The maximum velocity amounts to 0.001cm/sec or a little smaller. A marked pair of upflow and downflow is found respectively under Africa and the Central Pacific Ocean. The well-known non-dipole low over the Pacific area may have something to do with the downflow of the core material beneath there.