We propose an adaptive integral-type fixed-time stabilized sliding mode (IFSSM) control approach to simultaneously solve the control problems of state synchronization and anti-synchronization between two space-clamp FitzHugh–Nagumo (SFHN) neuro-cell circuit systems or neuronal circuits. The novel IFSSM consists of the fractional-powered, proportional, and integral terms of two state variables. The special characteristic of the IFSSM is that, on a sliding surface, one of the state variables becomes stable at a fixed time, then the other state variable is exponentially stabilized in sequence. Furthermore, two theorems related to the stability are provided and proven to demonstrate that the designed control approach can achieve the control goal. Numerical simulations are carried out to verify the validity of the proposed control approach for future practical realization in neuronal circuits. The developed control schemes can be implemented by the hardware circuit realization with voltage-sensing equipment.