The power distribution networks suffer from harmonic distortion, low power factor, voltage unbalance, and instability under nonlinear loads, which cause the degradation of power quality and the reliability of the grid. Existing methods, such as adaptive neural networks and model predictive control used in Distributed Static Compensators (DSTATCOMs), commonly suffer from slow convergence, high computational cost, and noise sensitivity, which limits their real-time performance. To deal with these problems, a Quasi-Hebbian least mean square (QHLMS) coordinated control strategy for DSTATCOMs is proposed in this paper. The QHLMS algorithm is superior in parallel processing, accurate weight adaptation, fast computation, strong convergence, and small steady-state error. In addition, its mathematical model is simplified into six subnets to reduce the complexity of the network. The proposed method for pulse generation is implemented in MATLAB/Simulink to realize the better compensation. Simulations compare QHLMS with adaptive least mean square (ALMS) algorithm and demonstrate substantial reduction in total harmonic distortion 3.95%, improvement in DC-link voltage regulation 580 V, and the decrease in DSTATCOM rating from 9.288 kVA to 7.7.855 kVA. These results are verified by hardware validation on dSPACE1104 under different loads and are in compliance with IEEE-519-2017, IEC-61727 and IEC-61000-1 standards.