A numerical controller having an interference prevention function whereby calculation for preventing interference is reliably performed. The numerical controller has the function of defining interference regions corresponding to multiple machine structural objects, respectively, moving the interference regions in accordance with machine coordinate values of the machine structural objects updated by interpolation, and performing an interference check to determine whether or not the interference regions interfere with each other. Interference check computation period automatic adjusting means automatically adjusts an interference check computation period, based on the value obtained by dividing a computation time required for the interference check by time of occupancy of the interference check within one interpolation period. Interference region expanding means expands the interference regions, based on the highest of feed velocities of respective axes and the interference check computation period. Checking means determines whether or not the expanded interference regions interfere with each other.