The invention relates to a GIL sliding support device and a GIL power transmission system. The GIL sliding support device comprises a mounting bracket and a bus cylinder bracket, a left guide groove and a right guide groove are formed in the mounting bracket at intervals in the left-right direction; the bus cylinder bracket is provided with a left guiding part and a right guiding part which are movably assembled in the corresponding guide grooves in a guiding mode, and a reserved gap for the bus cylinder bracket to move in the left-right direction is formed between at least one of the left guiding part and the right guiding part and the groove bottom of the corresponding guide groove. The guide groove is formed in the mounting bracket, so that the bus cylinder bracket can move in the front-back direction through the matching of the guiding parts and the guide grooves; by arranging the reserved gap between the left guiding part and the groove bottom of the corresponding guide groove, the bus cylinder can move in the left-right direction, that is, the bus cylinder can move in the axial direction of the bus cylinder and can also move in the radial direction of the bus cylinder, the flexibility of the bus cylinder is improved, damage to a bus shell is avoided, and normal operation of the device is guaranteed.