The invention discloses a bionic rigid-flexible coupling variable-rigidity continuum robot and a control method, the continuum robot comprises a machine body, continuum mechanisms, a main framework, a rigidity adjusting mechanism, a driving mechanism, a sensor unit, a control processing module and a power module, and the continuum mechanisms comprise a first continuum mechanism, a second continuum mechanism and a third continuum mechanism; each rigid mechanism is composed of a plurality of circular rigid section pieces, an elastic rod and a compression spring, each rigidity adjusting mechanism is composed of a plurality of sets of friction sliding blocks, springs, pressing blocks, pull rods, connecting rods, connecting shafts, rotating discs, torsional springs and pull ropes, and the control method comprises a pose control method and a rigidity control method. The continuum robot has the advantages of being compact in structure, light, flexible, controllable in rigidity and the like, and winding and grabbing of objects can be achieved.