The stabilities, structural, electronic and elastic properties of hypothetical TiX2B4 (X=Li, Na, Mg and Ca) crystalline structures obtained by replacing titanium atoms, which are located 4j Wyckoff positions in Ti3B4 with Ta3B4-type structure, with Li, Na, Mg and Ca. have been investigated by performing first-principles density functional theory calculations. It is shown that calculated formation enthalpy values of all compounds are negative, and thus designed compounds are energetically stable. However, single crystal elastic constants are calculated, and except for X=Na including compound, these constants supply required criteria, therefore it is determined that TiX2B4 (X=Li, Mg and Ca) compounds are mechanically stable. On the other hand, electronic band structures of stable compounds are calculated, and it is observed that all of the compounds have metallic character. Finally, atomic charge and bond overlap population information obtained from Mulliken analysis by combining 3-dimensional electron density characteristics, bonding nature of the compounds are studied.