Hybrid organic-inorganic perovskites show large potential applications in solar cells, light emitting diodes and low threshold lasers because of the high tolerance of defects compared with other semiconductor materials. Normally they have been synthesized by dilution method, generating a device with high performance, but they also introduce lots of defects. So far, investigations have been done intensively on ensemble defects both in theory and experiment, but single-defect related trapped excitons are yet to be explored. In this work, we prepared high-quality CH₃NH₃PbBr₃ perovskite nanowires with the length of about 1 μm and the width of several hundred nanometers by “reverse” ligand assisted reprecipitation method, and performed the magneto-photoluminescence measurement of different trapped excitons in single perovskite nanowires at a low temperature with a standard confocal microscopic system. The photoluminescence (PL) peak with narrow linewidth has been observed from trapped excitons with high luminescence intensity and the trapped excitons can be coupled with phonons in different ways. Both Zeeman splittings and diamagnetic effects have been observed in single trapped excitons under the magnetic field, and we found that the different trapped excitons have different Zeeman splittings and diamagnetic effects which is caused by the different defects near the trapped excitons. At the same time, we have extracted the g-factor of the trapped excitons under different magnetic field angles. The extracted exciton g-factors show anisotropic, which can be ascribed to the limitation of the lattice structure of the perovskite and the trapped exciton wave-function anisotropy under a vector magnetic field. Our results demonstrate that trapped excitons with narrow linewidth have very good luminescence properties and studying the magneto-optical properties from single trapped excitons can provide a deep understanding of trapped excitons in perovskites for applications in quantum light sources and spintronics. Furthermore, our results can also provide a possibility to control the electron spin in single-trapped-excitons-based hybrid organic-inorganic perovskites by manipulating the g-factor through an applied vector magnetic field, which promotes the application of the perovskite-based spintronics.