Provided is a control apparatus for a continuum robot system includes: a continuum robot (1), which includes a plurality of curvable portions (111, 112) provided in series in a longitudinal axial direction thereof and each being curvable, and is capable of being moved in the longitudinal axial direction; a drive unit (2) configured to move the continuum robot (1) in the longitudinal axial direction; and a plurality of angle control motors (211, 212) configured to change a distal-end angle (θ1, θ2) for each of the plurality of curvable portions (111, 112). The control apparatus includes a drive unit speed calculation/control unit (44) configured to calculate a followable speed, and to control the drive unit (2). The drive unit speed calculation/control unit (44) controls the drive unit (2) to move the continuum robot at a speed equal to or lower than the followable speed.