An object of the present invention is to provide a numerical controller that performs interference check based on a look-ahead position before a feedrate varies by taking the variation in the feedrate into consideration and controls the change of an override safely. To achieve this object, the numerical controller is configured such that, when calculating a coordinate value of a look-ahead position which a movable part subjected to interference check reaches after a look-ahead period elapses from a current position at a current time, the numerical controller calculates the look-ahead position assuming that the movable part moves at a predetermined feedrate of which the upper limit is the maximum feedrate.