In order to explore the vibration mechanism of vibration damping composite floor slabs and further enrich the theory of floor slab vibration calculation, the free vibration characteristics of vibration damped composite floor slabs and the dynamic response of vibration damped composite floor slabs under multi-source excitation is analyzed using first type Chebyshev polynomials to construct the displacement function and derive an analytical solution. The three-dimensional laminated theory is employed, considering the interlayer interaction. Based on the proposed method, the influences of loading types, positions, magnitudes, and frequencies on the vertical vibration of floor slabs are calculated. The study illustrates that, under the action of multi-source excitation, the displacement and acceleration responses calculated by the method proposed in this paper are always greater than those calculated by the single-plate theoretical solution. The dynamic responses of the vibration damping composite floor slab decrease with the increase of the thickness and elastic modulus of the vibration damping layer. Under different thicknesses of the vibration damping layer, the peak accelerations of the vibration damping composite floor slabs increase linearly with the growth of the load amplitude. In addition, the load movement path has a significant effect on the vibration response of the floor slab. When the moving load moves along the short side of the floor, the displacement response of the floor is generally greater than that along the long side of the floor.