A new method of 3D transient eddy current field calculation is proposed.The Maxwell equations with time component elimination (METCE) are derived under the assumption of magnetic quasi static approximation,especially for the sample of low conductivity.Based on METCE,we deduce a more efficient reconstruction algorithm of a 3D transient eddy current field.The computational burden is greatly reduced through the new algorithm,and the computational efficiency is improved.This new algorithm decompounds the space-time variables into two individual variables.The idea is to solve the spatial vector component firstly,and then multiply it by the corresponded time component.The iterative methods based on METCE are introduced to recover the distribution of conductivity in magneto-acoustic tomography.The reconstructed images of conductivity are consistent with the original distribution,which validate the new method.