The dispersion equation for Love wave propagation in a layer lying over a half-space is derived. Both media are assumed to be transversely isotropic fluid-saturated poroelastic solids with principal axes perpendicular to the surface. The analysis is based on the Biot’s theory. The dissipation due to fluid viscosity is considered and therefore the dispersion equation is complex and intractable analytically. An iterative procedure is developed to solve this equation. Two situations are discussed in detail: (i) an elastic layer overlying a poroelastic half-space and (ii) a poroelastic layer lying over an elastic half-space. Dispersion curves and attenuation curves of Love waves are plotted for these two cases. In addition, the upper and lower bounds of Love wave speeds are also explored.