Electromagnetic flow meters (EMFMs) are the gold standard in measuring flow velocity in process industry. The flow meters can measure the mean flow velocity of conductive liquids and slurries. A drawback of this approach is that the velocity field cannot be determined. Asymmetric axial flows, often encountered in multiphase flows, pipe elbows and T-junctions, are problematic and can lead to serious systematic errors. Recently, electromagnetic flow tomography (EMFT) has been proposed for measuring velocity fields using several coils and a set of electrodes attached to the surface of the pipe. In this work, a velocity field reconstruction method for EMFT is proposed. The method uses a previously developed finite-element-based computational forward model for computing boundary voltages and a Bayesian framework for inverse problems. In the approach, the vz-component of the velocity field along the longitudinal axis of the pipe is estimated on the pipe cross section. Different asymmetric velocity fields encountered near pipe elbows, solids-in-water flows in inclined pipes and in stratified or multiphase flows are tested. The results suggest that the proposed reconstruction method could be used to estimate velocity fields in complicated pipe flows in which the conventional EMFMs have limited accuracy.