Electromagnetic flowmeters, which have been one of the standard instrument to measure liquid flow rate in industry, are applied to tomographic imaging of flow velocity field. A flow meter has a flow signal which is proportional to the flowrate when the velocity profiles in the liquid is axisymmetric. Although some non-uniform magnetic field reduces the effect of axial non-symmetricity, the ideal field which induces the signal proportional to the flow rate free from velocity profile does not exist. Conversely, it is possible to evaluate velocity profiles through the proper design of the magnetic field. In this paper, we propose a new design of the 3D field excitation with two sets of eight magnetic poles and of eight signal pick-up electrodes. From the simulation study under a laminar swirling flow, that the reconstruction of 3D velocity distribution can be achieved from the induced signals.