Due to its high energy storage density, high instantaneous power, quick charging and discharging speeds, and high energy conversion efficiency, flywheel energy storage technology has emerged as a new player in the field of novel energy storage. With the wide application of flywheel energy storage system (FESS) in power systems, especially under changing grid conditions, the low‐voltage ride‐through (LVRT) problem has become an important challenge limiting their performance. In this paper, we propose a machine‐grid side coordinated control strategy based on model predictive current control (MPCC) for the insufficient LVRT capability of traditional FESS during grid faults. Excellent dynamic properties are demonstrated by the technique, which allows the grid‐side converter output current to swiftly follow the reference current instruction. The FESS's LVRT capability is increased when the grid‐side converter uses the MPCC current inner loop rather than the proportional–integral current inner loop during grid voltage dips. This greatly increases the reactive power response speed and efficiently supports the quick recovery of grid voltage. According to simulation verification carried out by Matlab/Simulink, the suggested control approach can assure the long‐term dependable operation of the FESS during voltage dips. This study can also be used as a reference for improving the FESS's LVRT capabilities in the future.