The vibrational excitations of linear tetratomic molecules, including both stretching and bending vibrations, are studied in the framework of U(4) algebra. Using Lie algebra, we get the algebraic Hamiltonian that consists of not only Casimir operators but also Majorana operators M₁₂, M₁₃ and M₂₃ which are indispensable for getting the potential energy surface and the force constants of linear tetratomic molecules in algebraic approach, and using this algebraic Hamiltonian, the highly excited vibrational levels of linear tetratomic molecules C₂HF and C₂D₂ are obtained. In addition, some other properties are also discussed.