The invention discloses a device and method for delivering a core of an injection well. The device comprises a sealing joint, a central rod and a lock claw. The sealing joint is arranged at the upper end of a wellhead blowout-prevention pipe, the central rod is sleeved with the sealing joint in a vertical-penetrating mode, the lock claw is connected to the lower end of the sealing joint and arranged on the outer side of the lower segment of the central rod in a sleeved mode at the same time, the outer side face of the lower end of the central rod and the inner side face of the lower end of the lock claw are designed to be corresponding conical surfaces, the conical inner side face of the lock clamp is rigidly extruded by the conical outer side face of the central rod through the axial movement of the central rod, and the lock claw is opened outwards and reset inwards. According to the device and method, the problem that the lower end of the core is extruded by an annular groove of a gate plate existing in the prior art, a gate cannot be normally opened, and downward delivering of the core is affected is solved.