First-principles calculations are performed to study the structural, electronic and magnetic properties of Co-doped SnO₂ nanosheets (NSs), using the generalized gradient approximation (GGA) plus Hubbard U method. We find that two Co atoms have a clustering tendency and the magnetic interactions between them exhibit a ferromagnetic (FM) coupling, while the appearance of an oxygen vacancy (V_O) turns it into an antiferromagnetic (AFM) order. When the Li atom is codoped into Co-doped SnO₂NS, the interactions between Co atoms are rehabilitated to FM coupling with a high Curie temperature (T_C) of 850 K. The electronic structure analysis reveals that this is mainly attributed to the hole-induced double-exchange mechanism from s–d hybridizations between Li and Co, which finally activates a long-range FM coupling between two Co atoms. These findings could be very useful in nano-material design for spintronics.