The structures and energies of the previously not studied titanium carbide TiCx (x = 3-4) clusters have been investigated by density functional theory (DFT) using the hybrid B3LYP functional in their singlet, tripler, and quintet potential energy surfaces. The planar four-membered ring structure VIs, otherwise called the "fan" structure, with a transannular Ti-C bond is the global TiC3 minimum and 21.5 kcal/mol more stable than the transannular C-C bond structure, VIIt ("kite" structure) at the DFT level. Both cyclic structures are energetically favored over a linear quintet minimum. Electronic structure and the nature of bonding in the various electronic states of the fan and kite structures of TiC3 have been well-characterized at the complete active space self-consistent field (CAS(12,12)) level. For the TiC4 cluster, two nonplanar structures have been considered in addition to three linear, fan, and kite geometries. Nonplanar structures are characterized as higher energy minima. The harmonic frequencies calculated using the DFT method for the Ti-C stretching vibrations in TiCx are in good agreement with the recent experimental results supporting the identification of new tetra- and pentaatomic titanium-carbon clusters.