The structural, elastic, electronic, and magnetic properties of the CrCoSi, MnCoSi parent half-Heusler (HH) alloys, and their CrMnCo2Si2 derivative double half-Heusler (DHH) compound are studied, utilizing the augmented plane wave method, which is based on density functional theory and implemented in the WIEN2k code. The stability of HH structure of the CrCoSi and MnCoSi alloys has been checked for their non-magnetic and ferromagnetic phases, leading to that the latter phase of the type I arrangement is the most stable. The CrMnCo2Si2 DHH alloy, derivative from the found structural and magnetic ground states of CrCoSi and MnCoSi HH alloys, is constructed and investigated. This DDH as well as its CrCoSi parent HH are found to be resistant to deformation and can be classified as ductile materials, whereas the MnCoSi compound is brittle. By the gradient generalized approximation (GGA), the electronic structures of CrCoSi, MnCoSi, and CrMnCo2Si2compounds exhibit a metallic behavior in the spin-up channel and a semiconducting behavior in the spin-dn channel, with band gaps (half-metallic gaps) of 0.851(0.020), 0.852(0.021), and 0.531(0.002) eV, respectively. The half-metallicity of CrMnCo2Si2 DHH is retained with smaller (larger) band gap (half-metallic gap) of 0.38(0.106) eV than that of GGA, using GGA + U approximation. In addition, the total magnetic moments are found to be 1, 2, and 3 µB for CrCoSi, MnCoSi, and CrMnCo2Si2, respectively. Therefore, these alloys can be good candidates for spinitronic applications due to their half-metallicity.