The influence of dephasing on the quantum spin Hall effect (QSHE) appearing in 2D topological insulator (TI) is studied. In the absence of dephasing, the longitudinal resistance in a QSHE system exhibits the quantum plateaus. We find that these quantum plateaus are robust against the normal dephasing but fragile with the spin dephasing. Thus, these quantum plateaus only survive in mesoscopic samples. In addition, we define a new spin Hall resistance that also exhibits quantum plateaus. In particular, these plateaus are robust against any type of dephasings and therefore, survive in macroscopic samples and better reflect the topological nature of QSHE.

We also study the disorder effect on the transport properties in QSHE. We confirm that at a moderate disorder strength, the initially un-quantized two terminal conductance becomes quantized, and the system makes a transition to the novel topological Anderson insulator (TAI). Conductances calculated for the stripe and cylinder samples reveal the topological feature of TAI and support the idea that the helical edge states may cause the anomalous quantized plateaus. The influence of disorder is studied by calculating the distributions of local currents. Based on the above-mentioned picture, the phenomena induced by disorder in the quantum spin Hall region and TAI region are directly explained.