One-dimensional (1D) carbyne chain has the potential applications in the nanoelectronic devices due to its unique properties. Although some progress of the mechanical and thermal properties of 1D carbyne chain has been made, the physical mechanism of the strain modulation of atomic bond nature remains unclear. In order to explore the strain effects on the mechanical and related physical properties of 1D carbyne chain, we systematically investigate the strain-dependent bond nature of 1D carbyne chain based on the first-principles calculations of density functional theory and generalized gradient approximation. It is found that when the compressive strain is 16%, the bonding nature of 1D carbyne chain is changed, and the bond length alternation of single and triple bonds in 1D carbyne chain tends to zero, which originates from the difference in bond strength between single bond and triple bond. Moreover, 1D carbyne chain can change from semiconductor into metal when the compressive strain is 16% indicated by analyzing the band structure and related differential charge density. When the strain is 17%, the phonon spectrum has an imaginary frequency. Besides, when the ambient temperature is less than 510 K, the heat capacity of 1D carbyne chain decreases with strain increasing. However, more phonon modes will be activated at larger strains when the temperature is higher than 510 K, and the heat capacity is enhanced gradually with strain increasing. Also, the stiffness coefficient of 1D carbyne chain is larger than that of graphene and carbon nanotube. These results conduce to the fundamental understanding of atomic bond nature in 1D carbyne chain under different strains.