X-ray investigation and conducting and magnetic properties of a novel organic superconductor composed of an organic donor MDT-TS and an asymmetric I2Br- anion are reported, where MDT-TS is 5H-2-(l,3-diselenol-2-ylidene)-l,3,4,6-tetrathiapentalene. The X-ray oscillation photograph and the energy dispersion spectroscopy (EDS) measurements determine the composition to be (MDTTS)I0.85Br0.41, where the anion composition is approximately I2Br. The donor and the anion construct an incommensurate lattice similar to (MDT-TS)(AuI2)0.441. The magnetic susceptibility of the complex behaves anisotropically below 50 K, indicating an antiferromagnetic order, while a metal-insulator (M-I) transition is observed at a lower temperature, TMI = 30 K, Application of hydrostatic pressure suppresses the M-I transition, and a superconducting phase appears above 9.8 kbar. The midpoint Tc rises to 6.1 K under 13.8 kbar, which is the highest Tc among the MDT-TSF series salts. The asymmetric I-I-Br- anion reduces TMI by considerably influencing the incommensurate antiferromagnetic insulating state but does not destroy the superconductivity because the incommensurate lattice originally has a kind of random potential on the donors. Consequently, this is the first organic superconductor with an asymmetric linear anion.