2015 AIP Publishing LLC. Without breaking the topological order, HgTe/CdTe quantum wells can have two types of bulk band structure: direct gap type (type I) and indirect gap type (type II). We report that the strong nonlinear optical responses exist in both types of bulk states under a moderate electric field in the terahertz regime. Interestingly, for the type II band structure, the third order conductivity changes sign when chemical potentials lies below 10meV due to the significant response of the hole excitation close to the bottom of conduction band. Negative nonlinear conductivities suggest that HgTe/CdTe quantum wells can find application in the gain medium of a laser for terahertz radiation. The thermal influences on nonlinear optical responses of HgTe/CdTe quantum wells are also studied.