Transport of charge carriers in PrBa2Cu3O7−δ (PBCO) is often described by variable-range hopping (VRH). Until now the VRH mechanism was confirmed merely on the basis of a temperature dependence of the resistivity following Mott's law. In this article we show a positive magnetoresistance in PBCO thin films, depending exponentially on the applied magnetic field. This provides substantial additional evidence for a variable-range hopping transport mechanism. Both a strong-field and a weak-field magnetoresistance can be identified. At temperatures above 30 K we observe weak-field magnetoresistance, at 4.2 K we detect a transition from weak-field to strong-field magnetoresistance at a magnetic field of approximately 4.5 T. In the weak-field regime the radius of the localized wave function is only affected marginally by the applied magnetic field. In the strong-field regime the radius of the localized wave function decreases with increasing magnetic field. From the measurements in the strong-field regime we obtain an estimate for the two-dimensional density of localized states in the PBCO thin film of approximately 2×1013 1/eVm2.