On the basic of the first-principles calculations with strong-correlated correction, the electronic structures and magnetic properties of a II–II–V based diluted magnetic semiconductor (Sr,K)(Zn,Mn)2As2 are investigated within Perdew-Burke-Ernzerhof generalized gradient approximation. With local spins doped via isovalent (Zn2+, Mn2+) substitutions, Sr(Zn,Mn)2As2 system prefers antiferromagnetic ground state, caused by Mn–Mn superexchange interactions. Via off-stoichiometry (Sr2+, K+) substitutions, holes are introduced into (Sr,K)(Zn,Mn)2As2 system, resulting in the ferromagnetic spin responses for local moments, except for the most nearest neighboring Mn–Mn pair. The ferromagnetism of this diluted magnetic semiconductor originates from the competition between the direct anti-ferromagnetic superexchange interaction and the indirect ferromagnetic coupling mediated by Zener's p–d exchange interaction. Our calculations show that Zener's p–d exchange interaction depends on the location of K dopants. From the investigation on the magnetic properties of Mn clusters, it is found that the reduction of the measured Mn saturation moments is caused by the counteraction of the local moments of the most nearest neighboring Mn–Mn pair.