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An efficient finite-element method is presented to analyze the scattering from complex bodies of revolution buried or partly buried in layered lossy media. In the proposed method, high-order edge-based vector basis functions are used to expand the transverse field components and high-order node-based scalar basis functions are used to expand the angular component. A locally conformal perfectly matched layer (PML) by complex coordinate stretching for inhomogeneous medium is presented and used to truncate the computational domain. Such a kind of PML is very easy to implement in the numerical process and is able to enclose an arbitrarily shaped convex object in the spatial domain. Numerical examples are presented to demonstrate the accuracy and efficiency of the presented method.