Surface properties and stability of quasicrystal-related complex metallic compounds Ag-In-Ca has been studied theoretically. Optimal structures of surface is obtained by relaxing the atoms in a slab to their force-free positions by the first-principles method. It is found that, after relaxation, In is at topmost position near the vacuum, Ag intrudes into the bulk and Ca is located at intermediate layers between In and Ag. To simulate STM images for the slab model, we calculate the charge distribution constructed from the electronic states in an appropriate energy range. We find that bright contrast is observed on different subsets of the In sites on surface for the charge distributions calculated from occupied and unoccupied states. Roles of the low-lying unoccupied Ca-3d states and the sp-d hybridization on surface electronic structures are discussed.