Study of the effective viscosity of suspensions is not only of interest in science, but also of great practical relevance to industries, such as the petrochemical industry, food and nutrition, materials processing and so on. In this paper, an attempt is made to establish theoretically the correlation between the effective viscosity of suspensions and their microstructural features. Firstly, the method for microstructural characterization developed by Fan et al. will be introduced to describe effectively the particle distribution in a suspension, and then the analogy between viscosity and field properties will be used to develop a new approach for the effective viscosity of suspensions. The new approach considers implicitly the effects of size, shape, orientation and distribution of the solid particles within the suspension through the topological parameters. Therefore, it can be applied to a suspension containing solid particles with any size, shape, orientation and distribution. Compared with other models available in the literature, the present approach is more realistic and more versatile. It can be applied to both liquids containing solid particles with a very high viscosity, and porous suspensions where the second phase has a vanishing viscosity. Perhaps more importantly, the present approach can predict the well-known S-shaped log eta-volume fraction curve in the whole range of microstructures (from completely continuous to completely discontinuous) and is in better agreement with experimental results.