The electronic structure and the magnetic properties of a new diluted magnetic semiconductor false(italicSr,italicNafalse)false(italicZn,italicMn)2As2 have been investigated, using first‐principles calculations within the Perdew–Burke–Ernzerhof generalized gradient approximation. Compound SrZn2As2 is a CaAl2Si2‐type structure semiconductor with a direct bandgap of 0.57 eV at the Γ point. With spins doped via isovalent (Zn2+, Mn2+) substitutions, the normalSrfalse(italicZn,italicMn)2As2 system prefers the antiferromagnetic ground state, resulting from the Mn–Mn superexchange interactions. Via off‐stoichiometry (Sr2+, Na+) substitutions, holes are introduced into the false(italicSr,italicNafalse)false(italicZn,italicMn)2As2 system, resulting in the ferromagnetic spin responses for Mn–Mn pairs, except for the nearest‐neighboring Mn–Mn pair. Based on our calculations, the ferromagnetism in the II–II–V‐based diluted magnetic semiconductor false(italicSr,italicNafalse)false(italicZn,italicMn)2As2 originates from Zener's p–d exchange interactions between localized Mn spins and itinerant holes mediated by As atoms.