We propose a computational framework using surrogate models through five steps, which can systematically and comprehensively address a number of related stochastic multi-scale issues in composites design. We then used this framework to conduct an implementation in nano-composite. Uncertain input parameters at different scales are propagated within a bottom-up multi-scale framework. Representative volume elements in the context of finite element modelling (RVE-FEM) are used to finally obtain the homogenised thermal conductivity. The input parameters are selected by a top-down scanning method and subsequently are converted as uncertain inputs. Machine learning approaches are exploited for computational efficiency, where particle swarm optimisation (PSO) and ten-fold cross validation (CV) are employed for hyper-parameter tuning. Our machine learning prediction results agree well with published experimental data, which proves our computational framework can be a versatile and efficient method to design new complex nano-composites.