Metallic glasses offer novel physical, chemical and mechanical properties and have promising potential applications. Recently, exploring the structure and deformation mechanism of metallic glasses according to the rheological mechanical behavior in the nominal elastic region has been the object of intensive research. Physically the mechanical analogues of fractional elements can be represented by self-similarity spring-dashpot fractal networks. In light of the fractal distribution features of the structural heterogeneities, a fractional differential rheological model is introduced to explore the viscoelastic a behavior of metallic glasses in this paper. To investigate the viscoelastic deformation mechanism, carefully designed nanoindentation tests at ambient temperature are proposed in this study. Three kinds of metallic glasses with different Poisson's ratio and glass transition temperature, which have the chemical compositions of Pd40Cu30Ni10P20, Zr48Cu34Pd2Al8Ag8, and (Fe0.432Co0.288B0.192Si0.048Nb0.04) 96Cr4 are selected as the model materials. Experimental and theoretical results clearly indicate that in the nominal elastic region, these metallic glasses exhibit linear viscoelasticity, implying a loading rate-dependent character. Based on the fractional calculus and Riemann-Liouville definition, experimental results are analyzed by the fractional-differential and integer order rheology models respectively. According to the stability of the fitting parameters, here we show that the fractional-differential Kelvin model, which consists of a spring and a fractional dashpot element, can fit the experimental viscoelastic deformation data of the investigated metallic glasses better than that with integer order rheological model. The extracted elastic modulis E1 of the spring in the fractional-differential Kelvin model are comparable to those of samples measured by traditional methods. Such a similarity can be well explained by the mechanical analogue of fractal model proposed for describing the distribution features of the structural heterogeneities in metallic glasses. The rheological parameters obtained here including viscosity index A and fractional order are capable of reflecting the rheological features and the flowing tendency of the above-mentioned metallic glasses. It is found that there exists a clear relationship between the rheological parameters and the reduced glass transition temperature as well as Poisson's ratio, which is helpful for understanding the correlation between plasticity and Poisson's ratio from the micro-structural point of view. The current work provides a rheological model-structure-property relation that may be applicable to a wide range of glassy materials.