In the conventional semiconductor distributed Bragg reflector (DBR) lasers, to obtain stable single mode emission, the gain section should be short enough to make the free spectrum range larger than half of the bandwidth of the reflection plateau caused by the DBR. This constraint severely limits the threshold and the output power of the lasers. In this work, single mode terahertz DBR quantum cascade lasers (THz-DBR-QCLs) that break the above constraint are realized. The lasers are based on the ridge waveguide, and exploit a cleaved facet and a DBR mirror to construct the resonator. Exploiting the intrinsic narrow gain spectrum of the THz-QCL, we tailor the reflection spectrum of the DBR so that the high reflection plateau and the gain spectrum are partially overlapped, obtaining the THz-QCLs with single mode emission. Such strategy enables single mode emission with a significantly elongated gain section, far beyond the constraint of the free spectrum range. In experiments, we realize the single mode THz-DBR-QCLs, whose gain section is as long as 3.6 mm. The emission frequency is about 2.7 THz, and the side mode suppression ratio (SMSR) exceeds 25 dB. The measured threshold and temperature characteristics of the THz-DBR-QCLs are comparable to the Fabry-Perot THz-QCLs fabricated with the same material. Our work suggests a novel approach to realize the high performance single mode THz-QCLs.