By using first-principles method, we studied the relation between the arrangement of the MPn₄ chains and the electronic structures for Zintl Ca₅M₂As₆ (M = Sn and Ga) compounds. It was found that the connecting forms between the adjacent chains in Ca₅M₂As₅₆ play a key role in determining their thermoelectric properties. The appearing of As–As bonding or not between adjacent covalent MAs₄ chains mainly depends on the different electron configuration between Pn and Ga (or Sn). Such As–As bonding in Ca₅Ga₂As₆ results in a sharp peak of density of states near the conduction band minimum, which will dramatically increase its n-type Seebeck effect. Moreover, the calculated band decomposed charge density demonstrates that the As–As bonding leads to a high charge accumulating along the y-direction for n-type Ca₅Ga₂As₆. Combined with the high electrical conductivity along the covalent anion chain direction, a high electrical conductivity may exist in n-type polycrystal of Ca₅Ga₂As₆. On the other hand, the absence of As–As bonding in Ca₅Sn₂As₆ results in a sharp peak of density of states near the valence band maximum, which can enhance its p-type Seebeck effect. For Ca₅Sn₂As₆, the small anisotropy of electrical conductivity may induce the high electrical value for its p-type polycrystal. Consequently, polycrystalline n-type Ca₅Ga₂As₆ and p-type Ca₅Sn₂As₆ may have good thermoelectric performance.