In a nuclear reactor power control system, when a control rod or a safety rod drops into a nuclear reactor by a failure of a control rod drive mechanism, a power of a summing and averaging circuit which sums and averages measurements of neutron detectors is smaller than a value A preset by an operator of the nuclear reactor. The averaged value of the neutron detector outputs is compared with the preset value A, and if the difference therebetween exceeds a preset limit signal level B for the output drop, automatic withdrawal of the control rod is stopped, and if the difference is smaller than the limit signal level B for the power drop, the control rod is withdrawn by the amount corresponding to the power drop.