This paper presents an experimental investigation on the compressive failure strength of fibre-reinforced polymer-matrix composite plates under impact loading. A new viscoelastic split Hopkinson pressure bar (SHPB) is used to measure those properties. Experimental problems such as dispersion corrections in viscoelastic bars are analysed. Significant increases of the compressive failure strength with the strain rate are found. It is also observed that the failure strength is sensitively higher when the loading is in the fibre direction. It is then in agreement with theoretical and experimental results under quasi-static loading.