Low noise terahertz (THz) receivers based on superconducting niobium nitride (NbN) hot electron bolometer (HEB) mixers have been designed, fabricated and measured for applications in astronomy and cosmology. The NbN HEB mixer consists of a planar antenna and an NbN bridge connecting across the antenna's inner terminals on a high-resistivity Si substrate. To eliminate the influence of direct detection and instability of the local oscillation (LO) power, a wire grid has been used to change the input LO power for compensating the shift of bias current during Y-factor measurement. The double sideband (DSB) receiver noise temperatures at 4.2 K without corrections have been measured from 0.65 to 3.1 THz. The excess quantum noise factor β of about 4 has been obtained, which agrees well with the calculated value. Allan variance of the HEB has been characterized, and Allan time TA longer than 0.4 s is obtained. We also estimated the temperature resolution of the HEB from the Allan variance and obtained the minimum temperature resolution of 1.1 K using a Gunn oscillator with its multipliers at 0.65 THz as an LO source.