Provided is a box-culvert relay push system (100) having a push apparatus and a box-culvert push block connection structure. The box-culvert relay push system (100) is arranged to push a box culvert (20) into a tunnel (200), and comprises a work platform (10) arranged adjacent to a tunnel entrance (210), and at least two sections of box culvert (20) located on the work platform (10); the box-culvert relay push system (100) also comprises at least one push apparatus (30) arranged to push the box culvert (20) located in front of the tunnel entrance (210), a pull apparatus (40) arranged to pull the second through n-th sections of the box culvert (20) in a first direction, and a pushing-force apparatus (50) arranged to push the box culvert (20) which is already partially or entirely inside the tunnel entrance (210); the pull apparatus (40) is connected between two adjacent box culverts (20), and the push apparatus (50) is arranged between two adjacent box culverts (20); each of the box culverts (20) is provided with a push-block structure (22), and the push apparatus (30) is arranged on the work platform (10) and is connected to the push-block structure (22) of one box culvert (20).