HfAl4C4, a new ternary aluminum carbide, was discovered and its crystal structure was determined by a combination of X-ray diffraction, transmission electron microscopy, and first-principles calculations. The crystal structure is trigonal belonging to the P (3) over bar m1 space group. The refined lattice constants are a50.3308 nm, c=2.190 nm. First-principles method was used to calculate the theoretical second-order elastic constants, bulk modulus, shear modulus, and the Young's modulus of HfAl4C4. It shows that HfAl4C4 has relatively high elastic stiffness.