The folding process of the 20 residue Trp-cage mini-protein was investigated using standard temperature replica exchange molecular dynamics (T-RexMD) simulation and a biasing potential RexMD (BP-RexMD) method. In contrast to several conventional molecular dynamics simulations, both RexMD methods sampled conformations close to the native structure after 10-20 ns simulation time as the dominant conformational states. In contrast, to T-RexMD involving 16 replicas the BP-RexMD method achieved very similar sampling results with only five replicas. The result indicates that the BP-RexMD method is well suited to study folding processes of proteins at a significantly smaller computational cost, compared to T-RexMD. Both RexMD methods sampled not only similar final states but also agreed on the sampling of intermediate conformations during Trp-cage folding. The analysis of the sampled potential energy contributions indicated that Trp-cage folding is favored by both van der Waals and to a lesser degree electrostatic contributions. Folding does not introduce any significant sterical strain as reflected by similar energy distributions of bonded energy terms (bond length, bond angle and dihedral angle) of folded and unfolded Trp-cage structures.