The structural properties, the formation enthalpies, and the mechanical properties of Co–Al compounds (CoAl, CoAl3, Co3Al, Co2Al5, Co2Al9, and Co4Al13) are studied by using Chen's lattice inversion embedded-atom method. The potential is transferable and therefore does well for studying different Co–Al compounds. The calculated lattice parameters and cohesive energies are consistent with the experimental and theoretical results. The formation enthalpies of all the Co–Al compounds are negative; therefore, the chemical bonding between Co and Al atoms increases the stability of compounds. According to elastic constant restrictions, all the six Co–Al compounds are mechanically stable. CoAl alloy with the larger moduli and lower Poisson's ratio is the hard or brittle phase. Moreover, CoAl3, Co3Al, Co2Al5, and Co2Al9 alloys are considered to be ductile materials, which have lower ratio of shear modulus to bulk modulus.