A detailed investigation of the steady-state and time-resolved spectral properties of new cationic asymmetrical trimethine cyanine dye with indolenine and benzoimidazole terminal groups has been performed in comparison with its symmetrical analogues. Steady-state measurements included absorption, fluorescence, excitation anisotropy in several solvents of different polarity and viscosity. Kerr-gated time-resolved study of the fluorescence properties has been performed using 1kHz femtosecond laser system. Experimental results are in agreement with DFT/6-31(d,p)/B3LYP quantum chemical calculations, allowing determination of the charge distribution, bond length alternation, permanent and transition dipole moments, energy levels and the leading molecular orbital configurations responsible for the lowest electronic transitions.