Small indium-doped carbon clusters InCn+(n=110) are systematically studied by the density functional theory at the B3 LYP/LANL2 DZ level. The computed properties include equilibrium geometries, electronic energies, vibrational frequencies, dipole moments and rotational constants for individual species. The calculation results show that the open-chain linear isomers with the indium atom bound to the end of the carbon chain are the most stable geometry in all cases. There must exist a cyclic or fan structure in the metastable or the third stable structure of cluster. The bigger the size of the cluster, the more obvious the stability of the structure is. The electronic ground state is found to be alternately a triplet for even n and a singlet for odd n with the only exception of InC+. It is generally observed that the spin contamination is not serious for all electronic ground states because the s2 values are uniform and in general deviate slightly from the pure spin values, and the B3 LYP wave functions are nearly spin-pure. It is also found that in the lowest-energy linear structure, the InC bond is longer (from 2.319 to 2.850 ) than the corresponding CC bonds in a range from 1.268 to 1.360 . The CC distances can be assimilated to moderately strong double bonds underlying a clear bonding in the corresponding structures. In addition, we observe a clear alternation in CC distances. The CoddCeven distances are shorter than the CevenCodd ones which mainly results from the charge distribution and spin density. According to the calculation and analysis of the incremental binding energy and the second difference we can deduce an even-odd alternation in the cluster stability for the linear InCn+, with their n-odd members being more stable than the adjacent even-numbered ones. This parity effect also appears in the adiabatic ionization potential curves. The analysis of magnetic properties shows the even-odd alternation with n-even clusters presenting higher values of magnetic moment than n-odd ones. The study of the polarizability indicates that the average values of both the polarization tensors and the anisotropic invariants increase with the size of cluster increasing.