Pulsar-like compact stars have strong magnetic fields, with the strength from \(\sim 10^9\) to \(\sim 10^{12}\) Gauss. How can such strong magnetic fields be generated and maintained is still an unsolved problem, and in principle it is related to the interior structure of compact stars. In this paper we propose that, under the Coulomb repulsion, the electrons in solid quark-cluster stars could spontaneously magnetized, and hence electrons could contribute non-zero net magnetic momentum to the whole star. We find that, for most cases in solid quark-cluster stars, the amount of net magnetic momentum, which is proportional to spin polarization \(\xi=(n_+-n_-)/n_e\) and depends on the number density of electrons \(n_e=n_++n_-\), could be significant with non-zero \(\xi\), and the corresponding magnetic moment per unit mass could be higher than \(10^{-4}\) Gauss cm\(^3\) g\(^{-1}\). Therefore the net magnetic moments of electron system in solid quark-cluster stars could be large enough to induce the observed magnetic fields for pulsars.