The most stable structure of the thinnest tungsten (W) nanowire with the radius of 1.9 angstrom was predicted by the simulated annealing basin-hopping method (SABH) with the tight-binding (TB) potential and the penalty algorithm. At this small scale, the predicted tungsten nanowire is helical instead of in the BCC arrangement found in bulk tungsten material. The density functional theory (DFT) calculation on the uniaxial tensile simulation was carried out to obtain the stress-strain profile of the thinnest tungsten nanowire. From the stress-strain curve, the Young's modulus is about 7.3% lower than that of bulk W, and the yielding stress is about 31 times higher than that of bulk W. The adsorption energy variations of an O-2 molecule on the top site of W atom at strain of 0 and 0.043 were used to explore the axial strain effect on the electronic properties of the thinnest W nanowire within the elastic region. Because the d-band center of the thinnest W nanowire at the strain of 0.043 becomes slightly closer to the Fermi level than that at strain of 0, the W atom of strained W nanowire becomes more reactive, resulting in the higher adsorption energy and the shorter W-O bond length. The density functional theory molecular dynamics (DFT-MD) simulation for the temperature elevation process was carried out for understanding the thermal stability of the thinnest W nanowire. The result shows the considerable deformation of local structure occurs at the temperature higher than 860 K, indicating the thinnest W nanowire can be safely used at the temperature lower than 860 K.