The harmonic oscillator model, which can be analytically solved, takes an important part in physics and is a powerful theoretical model for describing many physical processes. However, the research on driven harmonic oscillator is rarely involved. In this paper, we study the exact classical and quantum dynamics of two coupled harmonic oscillators in the driving external fields. In the framework of classical mechanics, the exact energy values of the time-dependent external fields acting on two coupled harmonic oscillator systems are obtained by virtue of the Hamiltonian canonical equations. If the driven fields are constant, the energy eigenvalues and eigenstates of the system in quantum mechanics are attained. In consideration of the time-dependent driven fields, the expected energy values and wave function of quantum system are derived using operator algebra methods. Because the microscopic particles have wave-particle duality within the framework of quantum mechanics, there are obvious differences between the classical and quantum dynamics for the system consisted of the two coupled harmonic oscillators in the external driving fields.