This study examines the effect of mixing varying percentages of nano-silica (NS), i.e. 2, 4 and 6% (by weight of polymer-modified bitumen, PMB) with PMB, in unaged and aged conditions. The Fourier transform infrared spectroscopy, x-ray diffraction, scanning electron microscopy and dynamic shear rheometer were used to determine chemical, microstructure and rheological properties of the binders, respectively. An artificial neural network (ANN) model, known as the multilayer perceptron neural networks model with three different algorithms namely; Levenberg-Marquardt (LM), scaled conjugate gradient (SCG), and gradient descent with adaptive back propagation (GDA) were used to predict the rheological properties of binders. The results indicate that adding NS to PMB may weaken the binders and delay their ageing. The amorphous structures of NS-PMBs remain unchanged and no new crystalline phase was formed when varying percentages of NS was added to PMB. Extreme heat caused a marked increase in the complex modulus of NS-PMB6 while low temperatures reduced its complex modulus. This resulted in enhanced resistance to the rutting and fatigue parameters. Adding higher amounts of NS particles to PMB also improved the viscoelastic properties and resistance to the ageing conditions of NS-PMB6. In terms of modeling, it was found that the most suitable algorithms and neurons number in the hidden layer for the ANN-Unaged model is LM algorithm and 11 neurons. For ANN-RTFOT and ANN-PAV models, the optimum algorithms and neurons number in hidden layer is SGC algorithm with 11 neurons and LM with 9 neurons respectively. The R-value (>0.95) for all models show a good agreement between measured and predicted data. It was concluded that the ANNs could be used as an accurate, fast and practical method for researchers and engineers to predict the phase angle and complex modulus of NS-PMBs.