bct-C4 carbon allotrope has been attracted great interest because its excellent mechanical properties. In this paper, we study the elastic properties and the strength properties of bct-C4 carbon by first-principles method. Our results show that bct-C4 presents a super uniaxial compressive strength of 524.3GPa, which is 6.9% more than the corresponding value of diamond. The high compressive strength originates from the high compressive rate of chemical bond deviating from compressive direction. Our work suggests that bct -C4 carbon can be widely used in the area of high pressure research.