The high flat-top pulsed magnetic field (HFPMF) refers to a magnetic field with a high intensity and a flat, stable region at its peak, which is critical for precision experiments. However, it is difficult to control and maintain the flat top of the magnetic field at high field strength with low ripple due to the magnet's significant current and dramatic heating. This paper proposes a system with a dual-coil magnet. It is supplied by a combination of capacitor banks, battery packs, and a set of generator-rectifier. Firstly, a dual-coil magnet is designed for the high field strength and long flat top of HFPMFs. Secondly, the circuit design is proposed with capacitors and battery packs in parallel to power the massive outer coil and the pulse generator-rectifier system to power the small inner coil. A novel control strategy is also proposed, with an open-loop control of the outer coil producing a slowly decreasing magnetic field and a closed-loop control of the inner coil to track the difference between the outer coil's magnetic field and the target magnetic field. Then the magnetic fields of both coils are superimposed to produce a long-lasting HFPMF. The power supply configuration is designed to address the energy requirements of the two coils and the drastic changes in resistance at different stages. Lastly, this research uses a system design and control implementation of 60 T/165 ms HFPMF to demonstrate the rationality and feasibility of this dual-coil combined power supply system.