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As the largest and most energetic single objects in the Universe comma giant radio galaxies openParGRGsclosePar comma are of particular interest as they are less common but extreme examples of radio source evolution. No unified model has emerged to explain the properties of this extreme class of radio galaxies. Previous studies of GRGs are mostly at radio and optical bands comma and there is a lack of systematic study of GRGs in X-rays. As the energetic radio jets of GRGs extend outwards comma they interact with the surrounding medium. We select a complete sample of nearby GRGs and propose new XMM observations to complete the X-ray coverage of the sample to study the X-ray properties of GRGs and their environments comma which helps to understand the processes responsible for the formation and evolution of GRGs.