The electronic structure, lattice vibrations, optical, dielectric and thermodynamic properties of BaTiO3/CaTiO3/SrTiO3 (BT/CT/ST) ferroelectric superlattices are calculated by using first-principles. The lattice parameters after relaxation are in good agreement with the experimental and other theoretical values within error of 1%. The band structure shows an indirect band gap with the value of about 2.039eV, and a direct band gap of 2.39eV at the Г point. The density of states and the electron charge density along [001] axis are calculated and show the displacement of Ti ions along the [001] axis. The strong hybridization between O 2p and Ti 3d contributes to the ferroelectricity of BT/CT/ST ferroelectric superlattices. The Γ modes are stable, while the vibration modes at A, M, R, and X point are unstable governing the nature of phase transition. The static dielectric tensor including the ionic contribution is calculated and the permittivity parallel to the optical axis is almost eight times more than the permittivity vertical the axis, exhibiting the strong anisotropy. The thermodynamic enthalpy, free energy, entropy, and heat capacity are also investigated based on the phonon properties.