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The phase stability and mechanical properties of tungsten borides W(2)B, WB, WB(2), W(2)B(5) and WB(4) were extensively studied by first-principles calculations within density functional theory. The thermodynamic and mechanical stabilities were examined. Our calculations on the enthalpy-pressure relationship and convex hulls have demonstrated that at zero pressure, the experimentally observed W(2)B-W(2)B (W(2)B-W(2)B represents W(2)B in W(2)B structure type, the same hereinafter) and WB-WB, and assumed WB(2)-ReB(2) phases are stable against decomposition into other components. The estimated hardness of WB(2)-ReB(2) is 39.4 GPa, suggesting that it is a potentially hard compound. At 60 GPa, the most stable phases are WB-WB and WB(2)-WB(2). WB-WB, WB(2)-AlB(2) and WB(4) are the ground state phases at 100 GPa. The phase transition mechanism for WB(2) was discussed. The synthesis of WB(2)-AlB(2) could be conducted at high pressures.