Bio-based materials have been extensively studied in recent decades. These materials based on vegetable aggregates are highly heterogeneous, and their complex behaviour depends on the behaviour of the constituents as well as their spatial distribution, size, and shape. Classically, homogenization methods are used for the prediction of the behaviour of heterogeneous materials because they allow to take into-account the microscopic phenomena and characteristics governing the macroscopic behaviour at a considered scale. In the case of composite materials, the use of this prediction approach allows to optimize the properties according to some criteria while limiting often expensive and time-consuming experimental tests. This paper aims to predict the effective thermal conductivity and model the mechanical behaviour of a bio-composite based on lime and cereal straw. A numerical homogenization approach was adopted to consider the complex microstructure of these biobased materials. An experimental characterization of the composites was carried out to describe the microstructure of the material (size, orientations, and shape of aggregates). X-Ray micro tomography observation was performed to determine volume fraction of the different phases of the biocomposite. A statistical approach was also used to determine the size of the Representative Volume Element (RVE) of the studied material for different distributions of heterogeneities. Then, numerical simulations of the thermal and mechanical behavior of composite was carried out. The results show the need to take into account an interphase between the straw aggregates and the matrix as well as the effect of the vegetal aggregates on the hydration of the binder to accurately predict the effective properties of the material.