First-principle self-consistent full potential linear augmented plane wave calculations based on density functional theory using hybrid functional PBE0 are performed to study magnetic moments, density of states and half-metallicity of L2 1 type full Heusler alloys with formula Co 2 Y Si. Y is Ti, V, Mn and Fe. We have compared these results with those of the PBE-GGA exchange correlation functional and the LDA + U method. The results for Co 2 FeSi and Co 2 MnSi are completely different; using the PBE0 hybrid functional for Co 2 FeSi predicts experimental magnetic moment and also predicts this material to be half-metallic ferromagnet, while using PBE-GGA predicts it not to be half-metal. The results of PBE0 are more similar to the ones obtained by LDA + U method.