We theoretically studied the structural, electronic, and magnetic properties in the two-dimensional (2D) AlN nanosheets (AlNNSs) doped with nonmagnetic (NM) atoms X(=Mg, Ca, Zn, and Sr), based on first principles calculations. The structure relaxations show Mg and Zn atoms locate in the 2D AlNNS plane, while the Ca and Sr atoms lie out of it. The results based on GGA-PBE scheme show that all the doped AlN monolayers (ML) are half-metallic. Further, results within HSE06 scheme show that Mg-, Zn- and Sr-doped AlN ML remain half-metallic while Ca-doped case changes into magnetic semiconductor. Each dopant induces a total magnetic moment of 1.0 mu(B) per supercell which mainly stemmed from the spin-polarized holes resided on the three nearest-neighboring N atoms. Calculations illustrate that ferromagnetic (FM) states are energetically stable when two X atoms separate far away from each other, while anti-ferromagnetic (AFM) states are energetically favorable when two X atoms locate at adjacent lattice sites. The long-range FM coupling and AFM one are attributed to the strong p-d/p-p interaction and the virtual hopping mechanism, respectively. Remarkably, because of the participation of the delocalized Zn-d orbitals in Zn-doped case, strong p-d/p-p interactions gain supremacy in the competition between virtual hopping mechanism and p-d/p-p interaction, resulting in FM coupling even two Zn atoms locate at close crystal lattice. Calculations show the two-X-doped AlNNSs have FM states with Curie temperatures (T-c) higher than 600 K, indicating that X-doped AlN systems are promising candidates for spintronic devices in the future. (C) 2016 Elsevier B.V. All rights reserved.