The influences of super Gaussian control pulse on dynamic gain response of the semiconductor optical amplifier (SOA) and switching characteristics of a terahertz optical asymmetric demultiplexer (TOAD) are studied in detail by considering the effects of gain saturation and recovery of SOA. The results are compared with the case of a Gaussian control pulse. It is shown that the super Gaussian control pulse will decrease the gain transition region of SOA and affect significantly the shape of the switching window of TOAD. When the time delay between the signal and control pulse is fixed, or the loop′s time asymmetry and the time delay between the signal and control pulse are all fixed, the maximum switching contrast of TOAD will be reduced due to the using of a super Gaussian control pulse.