A lithographic plate fastening apparatus of a printing press includes a pair of plate vises for fastening a mount plate to a plate cylinder, in a groove defined along the axis of the plate cylinder and includes a plate positioning reference pin provided on a clamping plate of a bite-side plate vise and tightly fitting a reference hole defined in a lithographic plate. The apparatus can rapidly, readily and accurately fasten a thinner lithographic plate e.g. paper plate to the plate cylinder.