The present invention relates to a remote, precise gap-measuring apparatus for automatically measuring the gap between reactor internals comprising a nuclear reactor vessel, a core support barrel, a core shroud and a lower support structure, the remote, precise gap-measuring apparatus comprising one and more digital probes measuring a gap between a nuclear reactor vessel protrusion and a core support barrel protrusion, the nuclear reactor vessel protrusions being disposed on an inner surface of the nuclear reactor vessel, the core support barrel protrusions being disposed on an outer surface of the core support barrel and engaged with the nuclear reactor vessel protrusions; a computer coupled to the digital probes to display and store a measured value of the gap measured by the digital probes; and a solenoid valve controlled by the computer, the solenoid valve controlling compressed air supplied through an air hose to operate the digital probe, wherein the digital probes measure the gap after the core support barrel, the core shroud and the lower support structure are welded to each other, thereby decreasing the construction period and simplifying the construction process.