The rational design of interfacial contacts plays a decisive role in improving interfacial carrier transfer and separation in heterojunction photocatalysts. In Z-scheme photocatalysts, the recombination of photogenerated electron–hole pairs is prevented so that the redox capacity is maintained. Here, one-dimensional graphitic carbon nitride (g-C3N4)/CoFe2O4 fibres were synthesised as a new type of magnetic Z-scheme visible-light photocatalyst. Compared with pure g-C3N4 and CoFe2O4, the prepared composite photocatalysts showed considerably improved performance for the photooxidative degradation of tetracycline and methylene blue. In particular, the photodegradation efficiency of the g-C3N4/CoFe2O4 fibres for methylene blue was approximately two and seven times those of g-C3N4 and CoFe2O4, respectively. The formation mechanism of the Z-scheme heterojunctions in the g-C3N4/CoFe2O4 fibres was investigated using photocurrent spectroscopy and electrochemical impedance spectroscopy. We proposed that one of the reasons for the improved photodegradation performance is that the charge transport path in one-dimensional materials enables efficient photoelectron and hole transfer. Furthermore, the internal electric field of the prepared Z-scheme photocatalyst enhanced visible-light absorption, which provided a barrier for photoelectron–hole pair recombination.