Echo state network (ESN) proposed by Jaeger in 2001 has remarkable capabilities of approximating dynamics for complex systems, such as Mackey-Glass problem. Compared to that of ESN, the scale-free highly-clustered ESN, i.e., SHESN, which state reservoir has both small-world phenomenon and scale-free feature, exhibits even stronger approximation capabilities of dynamics and better echo state property. In this paper, we extend the state reservoir of SHESN using leaky integrator neurons and inhibitory connections, inspired from the advances in neurophysiology. We apply the extended SHESN, called e-SHESN, to the Mackey-Glass prediction problem. The experimental results show that the e-SHESN considerably outperforms the SHESN in prediction capabilities of the Mackey-Glass chaotic time-series. Meanwhile, the interesting complex network characteristic in the state reservoir, including the small-world property and the scale-free feature, remains unchanged. In addition, we unveil that the original SHESN may be unstable in some cases. However, the proposed e-SHESN model is shown to be able to address the flaw through the enhancement of the network stability. Specifically, by using the ridge regression instead of the linear regression, the stability of e-SHESN could be much more largely improved.