The structural, electronic, and magnetic properties of the GaS monolayer doped by 12 different kinds of atoms were investigated systemically using first-principles calculations. N is found to be the most promising candidate for p-type doping among dopants at the S site, including nonmetal atoms H, B, C, N, O, and F and transition metal atoms V, Cr, Mn, Fe, Co, and Ni. Transition metal atoms appear to be hardly incorporated in the GaS monolayer under either S- or Ga-rich conditions. While the net magnetic moments of doped GaS by nonmetal atoms are either 0 or 1 mu(B), the value of transition metal dopants decreases from 5 to 0 mu(B) by adding the number of valence electrons from V to Ni. In the case of transition metal dopants at the Ga site, the majority spin states of Cr and Co are located closest to the conduction band minimum and valence band maximum, respectively. Magnetic ground states exist in all of the monolayers doped by these impurities. Indirect band gap of the pristine GaS monolayer is regulated to be direct from one type of spin channel by introducing B and Mn in the S site and V, Fe, Co, and Ni in the Ga site.