Theoretically, the grounded-wire transient electromagnetic method can obtain five different components in field measurements for deep ore deposit exploration. The electrical component usually offers high precision and detection depth as compared to the magnetic component due to stronger anti-noise ability, while the magnetic component has the merit of stability in the inversion process but is insensitive to the resistance body. Considering that the Gram constraint is a kind of generalised constraint, applied for components of non-linear relation, this paper proposes a joint constrained inversion method to combine the electrical and magnetic component data, which are inverted by a truncated singular value decomposition method. Finally, the conjugate gradient inversion method is applied to synthetic data and iron ore field data to demonstrate the improved result based on both the electrical and magnetic component.