Photoconduction in the monoclinic phase of quasi-one-dimensional conductor TaS 3 has been observed at T < 70 K. It was studied jointly with low-temperature ohmic and non-linear dark conduction. The strong sample quality dependence of both photoconduction and dark conduction at this temperature region has been observed. Together with a similarity of the main features of the photoconduction characteristic of both monoclinic (m-TaS 3 ) and orthorhombic (o-TaS 3 ) samples the following new peculiarities of photoconduction in m-TaS 3 were found: 1) the dependence of the activation energy of photoconduction on temperature, T , 2) the change of the recombination mechanism from the linear type to the collisional one at low T with a sample quality growth, 3) the existence of a fine structure of the electric-field dependence of photoconduction. Spectral study gives the Peierls energy gap value 2∆ * = 0.18 eV.