This paper basically concentrates on the bifurcation control of a fractional delayed predator–prey system via feedback control methodology. Firstly, time delay is regarded as a bifurcation parameter, and the delay-induced bifurcation conditions for such uncontrolled predator–prey system are established. Secondly, state feedback controllers are implemented to suitably control the Hopf bifurcation for the proposed system. Surprisingly, it is discovered that bifurcation control cost can be highly cut down by a single controller as compared with three. Particularly, the effects of control for the first feedback gain surpass the other two. The desirable dynamics can be acquired by cautiously selecting advisable feedback gains. Finally, numerical examples exhibit the theoretical analysis which coincides with the schemed methods.