The structural, thermodynamic, mechanical and electronic properties of 5d transitional metal diborides TMB2 (TM=Hf-Au) are systematically investigated by first-principles within density functional theory. For each diboride, three structures are considered, i.e., AlB2, ReB2 and WB2 structure. The calculated lattice parameters are in good agreement with previous theoretical and experimental results. From the calculated formation enthalpy, thermodynamic stability of compounds is predicted and the formation enthalpy increases from HfB2 to AuB2. Among the considered structures, AlB2 structure is the most stable for HfB2 and TaB2; ReB2 structure is the most stable for WB2, ReB2, OsB2, IrB2 and AuB2; WB2 structure is the most stable for PtB2. The ReB2 in ReB2 structure has the largest shear modulus (295 GPa), and is the hardest compound, which is in agreement with previous theoretical and experimental results. The calculated density of states shows that they are all metallic. Their variation trends are discussed.