A systematic study based on ab initio calculations within the local spin density approximation (LSDA) has been performed on the Ⅲ-Ⅴ semiconductors (GaAs and GaP) doped by the 3d-transition metals (TM=V, Cr, Mn, Fe, Co and Ni). It is shown that the ferromagnetic (FM) state will be realized when the GaAs and GaP are doped by V, Cr or Mn, however, the system is antiferromagnetic (AFM) when doped by Fe; whereas these dilute magnetic semicondutors(DMS's) show unstable magnetism when doped by Co or Ni. It is suggested that Ⅲ-Ⅴ semiconductors doped by Cr can be candidates for high Curie Temperature DMS. For the present systems, the magnetic moment of V ion is greater than the theoretical value, those of Fe, Co and Ni are smaller than theoretical values, whereas for those of Cr and Mn, the difference between TM's magnetic moment and the expected value depends on the crystal symmetry and electronic states of ions. Finally, we show that, by the co-doping of Si and Mn in GaAs and GaP, the DMS's present a more stable FM state and a higher TC.