The exact solution for incompressible and unsaturated porous media has not been provided in the current literature. Thus, an exact solution was derived in the present study for the transient response of single-layer, incompressible, and unsaturated porous media in one-dimension conditions with typical boundary conditions based on the wave equations for unsaturated porous media proposed by Zienkiewicz. The inertial, viscous, and mechanical couplings were considered in the proposed solution. Taking the relative displacement of the liquid phase fluid as an independent variable, the dimensionless governing equations were first derived, and the eigenvalue and eigenfunction of the undamped system were given. Then, the original problem was transformed into the initial value problem for a set of second-order ordinary differential equations based on the constant-transform method and the orthogonality of eigenfunctions. The resulting problem was then solved using the state-space approach. Through this process, the exact solutions for displacement and stress of the original problem were obtained. The correctness of the solutions was verified by comparing them with the existing analytical and numerical results. Specifically, the analytical results indicate that only one type of compression wave exists in the incompressible unsaturated porous media. The compression wave with an opposite phase to the incident wave was generated at the fixed displacement boundary, whose response amplitude revealed a decreasing tendency with the increase of porous medium saturation.