In a recent paper , a modified DeGroot-Friedkin model was proposed to study the evolution of the social-confidence levels of individuals in a reflected appraisal mechanism in which a network of n individuals consecutively discuss a sequence of issues. The individuals update their self-confidence levels on one issue in finite time steps, via communicating with their neighbors, instead of waiting until the discussion on the previous issue reaches a consensus, while the neighbor relationships are described by a static relative interaction matrix. This paper studies the same modified DeGroot-Friedkin model, but with time-varying interactions which are characterized by a sequence of doubly stochastic matrices. It is shown that, under appropriate assumptions, the n individuals' self-confidence levels will all converge to 1/n exponentially fast. An explicit expression of the convergence rate is provided.