We present a multidomain pseudospectral method for the accurate and efficient time-domain computation of scattering by body-of-revolution (BOR) perfectly electrically conducting objects. In-the BOR formulation of the Maxwell equations, the azimuthal dependence of the fields is accounted for analytically through a Fourier series. The numerical scheme in the (r, z) plane is developed in general curvilinear coordinates and: the method of characteristics is applied for patching field values in the individual subdomains to obtain the global solution. A modified matched-layer method is used for terminating the computational domain and special attention is given to proper treatment of the coordinate singularity in the scattered field formulation and correct time-domain boundary conditions along edges. Numerical results for monochromatic plane wave scattering by smooth and nonsmooth axis-symmetric objects, including spheres, cone-spheres, and finite cylinders, is compared with results from the literature, illustrating the accuracy and computational efficiency associated,vith the use of properly-constructed spectral methods. To emphasize the versatility of the presented framework, we compute plane wave scattering by a missile and find satisfactory agreement with method-of-moment (MoM) computations.