We study the entropy-corrected version of the holographic dark energy (HDE) model in the framework of modified Friedmann-Robertson-Walker cosmology. We consider a non-flat universe filled with an interacting viscous entropy-corrected HDE (ECHDE) with dark matter. Also included in our model is the case of the variable gravitational constant G. We obtain the equation of state and the deceleration parameters of the interacting viscous ECHDE. Moreover, we reconstruct the potential and the dynamics of the quintessence, tachyon, K-essence and dilaton scalar field models according to the evolutionary behavior of the interacting viscous ECHDE model with time-varying G.