Propagation of Love-type waves emanating due to a disturbance point source in a transversely isotropic layer of finite thickness laid over a semi-infinite half-space is investigated. The layer is assumed under the influence of magnetic field and hydrostatic state of stress, while the half-space is inhomogeneous. The source point is situated at the common interface of the layer and half-space. Maxwell’s equation and generalized Ohm’s law have been taken into account to calculate the Laurent force induced in the layer. Green’s function technique and Fourier transform are used as a powerful tool to calculate the interior deformations of the model; consequently, we obtain a closed-form dispersion relation for the wave. Six numerical examples for the transversely isotropic layer, namely, beryl, magnesium, cadmium, zinc, cobalt, and simply isotropic, have been considered. The role of magneto-elastic coupling parameter, hydrostatic stress, inhomogeneity, the order of the depth variation in inhomogeneity function, and different examples of the layer on the propagation of Love-type wave has been observed by numerical examples and graphical demonstrations. © The Author(s) 2018.