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The first principles calculations are carried out to understand the half metallic and ferromagnetic properties of Fe2−xCoxTiSi (x = 0, 0.5, 1, 1.5, 2) full Heusler alloys. The stable structure is predicted as L21 structure (Cu2MnAl phase). The lattice constant value of Fe2−xCoxTiSi Heusler compounds increases as the value of x increases. These alloys exhibit half metallic ferromagnetism (except Fe2TiSi) with small spin flip gap at the minority spin state. At high pressure, semiconductor to metallic phase transition is observed in Fe2TiSi while half metallic to metallic phase transition is observed in Fe1.5Co0.5TiSi, Fe1.0 Co1.0TiSi, Fe0.5Co1.5TiSi and Co2TiSi. The spin polarization of these compounds (except Fe2TiSi) is 100%. Hence, these compounds are suitable for spin injection devices in spintronics. [ABSTRACT FROM AUTHOR]