A feed speed control method for a numerical control device in which a feed speed of a tool traveling along an instructed machining path is controlled in accordance with a machining program. The speed of each axis is derived (S2), and the acceleration of each axis is derived from a speed variation between adjacent blocks (S3). When the acceleration (.DELTA.Vx) is larger than a permissible acceleration (.DELTA.Vxmax) (S4), first ratios (K1) of the permissible accelerations to the accelerations are derived for individual axes (S5), and the smallest of the first ratios is selected. The command speed is multiplied by the square root of the smallest first ratio to derive an actual feed speed (S9). In this way, shock to a machine is reduced and an excessive load on a servomotor is reduced even when blocks continue for successive infinitesimal distribution distances, as in the case wherein a curve is approximated by the use of straight lines.