Geomagnetic storms are one of the space weather events. The radio signals transmitted by modern navigation systems suffer from the effects of magnetic storms, which can degrade the performance of the whole system. In this study, the performance of the BeiDou Navigation Satellite System (BDS) B1 frequency standard point positioning (SPP) in China and the surrounding area during different classes of storm was investigated for the first time. The statistical analysis of the results revealed that the accuracy of the BDS-2 B1 frequency SPP deteriorated during the storms. The probability of the extrema of the positioning error statistics was largest during strong storms, followed by moderate and weak storms. The positioning accuracy for storms of a similar class was found not to be at the same level. The root mean square error in positioning for the different classes of storm could be at least tens of centimeters in the east, north and up directions. The findings in this study could contribute toward the error constraint of BDS positioning accuracy during different classes of geomagnetic storm and be beneficial to other systems, such as BDS-3, as well.