The effect of zirconium alloying on the crystal structures and mechanical properties of binary tungsten–zirconium alloys is investigated in this study using the first-principles method. Firstly, we investigate the cell volumes, lattice constants, and formation energies of binary W1−xZrx (x = 0, 0.0625, 0.125, 0.1875, 0.25, and 0.5) alloys. It is shown that binary tungsten–zirconium alloys maintain BCC structures. When the concentration of zirconium atoms is lower than 12.5%, the structures of binary tungsten–zirconium alloys can be thermodynamically stable. The elastic constants of binary tungsten–zirconium alloys are calculated based on the optimized atomic lattice. Then, the elastic modulus and other mechanical parameters are deduced according to the relevant formulas. It is shown that the mechanical strength of binary tungsten–zirconium alloy decreases with an increasing concentration of zirconium atoms, which is lower than the mechanical strength of pure tungsten metal. However, the mechanical strength of binary tungsten–zirconium alloys is higher than that of pure zirconium metal. In addition, zirconium alloying can be effective in improving the ductility of pure tungsten metal.