Based on the tight-binding model, we present the analytical expressions for the energy spectrum and Pauli susceptibility of zigzag graphene nanoribbons (ZGNRs). The influences of lattice site, temperature, and ribbon width on the Pauli susceptibility are discussed in detail. The results show that the Pauli susceptibility damps rapidly from the edge to bulk sites at a given finite temperature. In the low-temperature regime, the Pauli susceptibility exhibits a remarkable Curie-law-like behavior, while in the high-temperature regime it displays a normal paramagnetic behavior. As the ribbon width is increased, the Pauli susceptibility at each edge of a given ZGNR gradually increases to a saturated value. These novel magnetic properties of ZGNRs are closely related to edge states.