A molding machine management system includes: an injection molding machine including a mold, an injection unit, and a mold clamping unit; a management server coupled to the injection molding machine via a network; a first camera configured to capture an image of the mold; a second camera configured to capture an image of a drive unit provided in the injection molding machine; and a storage unit that stores first moving image data which is moving image data of the mold captured by the first camera, and second moving image data which is moving image data of the drive unit captured by the second camera, in association with a shot number of the injection molding machine. The management server includes a control unit configured to cause a display unit to display the first moving image data and the second moving image data in association with the shot number.