[en] The availability of a cooled antiproton beam in the energy range from 2.0 to 5.5 GeV will allow the P-barANDA experiment, planned for operation in FAIR (Darmstadt, Germany), to perform a wide nuclear and particle physics program. P-barANDA is the only experiment worldwide in that energy regime that combines a solenoidal magnetic field (B = 2 T) and a dipole field (maximum bending power equal to 2 Tm) in a fixed-target experiment. The offline tracking algorithm is developed within the PandaRoot framework, which is part of the FairRoot project. Here the GENFIT2 package is presented. The tool contains an implementation of the Kalman filter and the deterministic annealing filter for charged particle track reconstruction, together with a Runge-Kutta track representation. It also interfaces with Millipede II and RAVE, for alignment and vertex reconstruction, respectively. The performance of this track-fitting package for the P-barANDA experiment is shown for the first time, within the PandaRoot framework. For those channels where a good low momentum tracking is required, i.e. p_T c, an improvement by a factor of about two is shown