The propagator matrix method is developed to study the dynamic response of a multilayered poroelastic half-space to time-harmonic surface tractions. In a cylindrical coordinate system, a method of displacement potentials is applied first to decouple the Biot's wave equations into four scalar Helmholtz equations, and then, general solutions to those equations are obtained. After that, the propagator matrix method and the vector surface harmonics are employed to derive the solutions for a multilayered poroelastic half-space subjected to surface tractions. It is known that the original propagator algorithm has the loss-of-precision problem when the waves become evanescent. At present, an orthogonalization procedure is inserted into the matrix propagation loop to avoid the numerical difficulty of the original propagator algorithm. Finally, a high-order adaptive integration method with continued fraction expansions for accelerating the convergence of the truncated integral is adopted to numerically evaluate the integral solutions expressed in terms of semi-infinite Hankel-type integrals with respect to horizontal wavenumber. Furthermore, to validate the present approach, the response of a uniform poroelastic half-space is examined using the formulation proposed in this article. It is shown that the numerical results computed with this approach agree well with those computed with the analytical solution of a uniform half-space.