<p>The nonlocal viscous Cahn-Hilliard equation (NvCH) is a generalization of the classic viscous Cahn-Hilliard equation by replacing the Laplacian operator with a parameterized nonlocal diffusion operator and inherits the maximum bound principle (MBP), mass conservation, and energy dissipation law as its local counterpart. However, designing an efficient time-stepping scheme for the NvCH equation that unconditionally preserves these structures is a highly challenging task. In this paper, we first present and analyze a second-order exponential time differencing (ETD) Crank-Nicolson (CN) scheme for solving the NvCH equation, which unconditionally preserves the discrete MBP, energy dissipation, and mass conservation. Optimal error estimates and asymptotic compatible properties are rigorously established, illustrating that the numerical solutions of the NvCH equation converge to those of the local viscous Cahn-Hilliard equation (LvCH) as the horizon parameter, spatial mesh size, and time step size tend towards zero. Extensive numerical tests are also performed in two and three dimensions to validate the theoretical results and demonstrate the efficiency of the proposed scheme.</p>