Hygrothermal mathematical models are commonly used to describe heat and moisture transfer in porous and bio-based building construction materials. This allows to evaluate their thermal insulation capacity, as well as their ability to regulate external climatic conditions and ensure indoor comfort for inhabitants. In this paper, a sensitivity analysis is performed on Kunzel's model, while it is applied to simulate the hygrothermal behavior of a wall structure made of a new bio-based building material (cement composite including date palm fibers). In a first part, the effects of finite variations of material properties/boundary conditions on the model's outcome are investigated. In a second step, specific transfer modes are neglected in the model, in order to study their influence on the numerical predictions. The results of this parametric study show that special attention should be paid to few parameters (heat capacity and density for heat transfer, sorption isotherm and water vapor resistance factors for moisture transfer) at the expense of others. Uncertainties on these influent parameters may result in large error accumulation, especially when modeling the moisture transfer process. Furthermore, initial boundary conditions and sensors position appear to be possible sources of discrepancies in the calculated RH profiles. Finally, the pure conduction model is found to provide good estimation of the temperature profiles compared to the full model, whereas liquid transfer must always be taken into account in the model to ensure accurate RH predictions through a bio-based date palm concrete wall.