Density functional theory calculations were carried out to probe the nature of the electronic structure change in TiPO4 before and after its spin-Peierls distortion at 74.5 K, which is characterized by the dimerization in the chains of Ti3+ (d1) ions present in TiPO4. These calculations suggest strongly that the electronic state of TiPO4 is magnetic insulating before the distortion, but becomes nonmagnetic insulating after the distortion. Consistent with this suggestion, the phonon dispersion relations calculated for TiPO4 show that the undistorted TiPO4 is stable, while the distorted TiPO4 is not, if each Ti3+ ion has a spin moment, and that the opposite is true if each Ti3+ ion has no spin moment. These observations suggest that the driving force for the spin-Peierls distortion is the formation of direct metal-metal bonds leading to the dimerized chains of Ti3+ ions. The abrupt change in the electronic structures from a magnetic insulating state to a nonmagnetic insulating state explains why the spin-Peierls distortion of TiPO4 exhibits a first-order character. Although the two electronic states of TiPO4 before and after the distortion have a band gap, the substantial spin-Peierls distortion is found to enhance the thermoelectric properties of TiPO4.