Recent experiments and first-principles calculations in the literature revealed the existence of a C36 laves phase in the A12Ca-Mg2Ca pseudo-binary system in addition to the C14-Mg2Ca and C15-A12Ca laves phases. In the present work, special quasirandom structures (SQS) for all three laves phases were constructed. The structures possess local pair and multisite correlation functions that mimic those of the corresponding random structures. First-principles calculations were carried out based on the SQS developed to predict the enthalpy of formation in the A12Ca-Mg2Ca pseudo-binary system. It was observed that the enthalpy of formation of C36 is very close to that of C14 at the Mg2Ca end and decreases with the addition of small amount of Al, while the enthalpy of formation of C14 increases with the addition of Al. It is thus energetically plausible that C36 is stable in the A12C- Mg2Ca pseudo-binary system.