An excitonic insulator (EI) is an intriguing correlated electronic phase of condensed excitons. Ta2NiSe5 is a model material for investigating condensed excitonic states. Herein, femtosecond pump-probe spectroscopy is used to study the coherent phonon dynamics and associated exciton-phonon coupling in single-crystal Ta2NiSe5. The reflectivity time series consists of exponential decay due to hot carriers and damped oscillations due to the Ag phonon vibration. Given the in-plane anisotropic thermal conductivity of Ta2NiSe5, coherent phonon oscillations are stronger with perpendicular polarization to its quasi-one-dimensional chains. The 1-, 2-, and 4-THz vibration modes show coherent amplitude responses in the EI phase of Ta2NiSe5 with increasing temperature, totally different from those of normal coherent phonons (the 3- and 3.7-THz modes). The amplitude modes at higher frequencies decouple with the EI order parameter at lower temperatures, as supported by theoretical analysis with a model Hamiltonian of the exciton-phonon coupling system. Our work provides valuable insights into the character of the EI order parameter and its coupling to multiple coherent amplitude modes.