Automotive and aeronautical composite structures can be subjected to dynamic loading scenarios (e.g. crash, bird strike). In both industrial areas, energy-based damage models for composite materials, able to predict initiation and evolution of damage of a composite ply under various loading conditions, are increasingly used. These models require the specification of fracture toughness parameters for the main failure modes. In previous works [1],[2], the authors have successfully enhanced a methodology suggested by Catalanotti et al. [3],[4] to measure the fiber failure crack resistance curves of a UD carbon fiber composite under dynamic loading. This methodology uses the relation between the energy release rate, the crack resistance curve and the size-effect law. For the determination of the size-effect law, double-edge-notched specimens of different sizes are tested. In this work, the developed approach is used for the measurement of the fracture toughness for fiber tension and compression failure of a UD glass-epoxy composite under high rate loading. Static tests are performed on an electromechanical test machine. For the high rate tests, split-Hopkinson bars for tensile (SHTB) and compressive (SHPB) loading are used. The results show, that the fracture toughness of the UD glass-epoxy composite, associated with the fiber failure modes, increases with increasing loading rate for tension as well as for compression. The observed strain rate effect on the fracture toughness of the glass-epoxy composite is more pronounced than for the carbon-epoxy composite investigated in [1],[2], in particular for fiber tensile failure.