Biomedical applications of swimming microrobots comprising of drug delivery, microsurgery and disease monitoring make the research more interesting in MEMS technology. In this paper, inspired by the flagellar motion of microorganisms like bacteria and also considering the recent attempts in one/two-dimensional modelling of swimming microrobots, a three degrees-of-freedom swimming microrobot is developed. In the proposed design, the body of the swimming microrobot is driven by multiple prokaryotic flagella which produce a propulsion force through rotating in the fluid media. The presented swimming microrobot has the capability of doing three-dimensional manoeuvres and moving along three-dimensional reference paths. In this paper, following dynamical modelling of the microrobot motion, a suitable controller is designed for path tracking purposes. Based on the resistive-force theory, the generated propulsion force by the flagella is modelled. The feedback linearization method is applied for perfect tracking control of the swimming microrobot on the desired motion trajectories. It is seen that, by the use of three flagella, the microrobot is able to perform three-dimensional manoeuvres. From the simulation results, the tracking performance of the designed control system is perfectly guaranteed which enables the microrobot to perform the desired three-dimensional manoeuvres and follow the desired trajectory.