Here we investigate the mechanical properties and structural design of the pericarp of the green coconut (Cocos nucifera L.). The pericarp showed excellent impact characteristics, and mechanical tests of its individual components revealed gradients in stiffness, strength and elongation at break from the outer to the inner layer of the pericarp. In order to understand more about the potential effect of such gradients on 'bulk' material properties, we designed simple, graded, cellulose fibre-reinforced polylactide (PLA) composites by stacking layers reinforced with fibres of different mechanical properties. Tensile properties of the graded composites were largely determined by the 'weakest' fibre, irrespective of the fibre distribution. However, a graded design led to pronounced asymmetric bending and impact properties. Bio-inspired, asymmetrically graded composites showed a flexural strength and modulus comparable to that of the strongest reference samples, but the elongation at maximum load was dependent on the specimen orientation. The impact strength of the graded composites showed a similar orientation-dependence, and peak values exceeded the impact strength of a non-graded reference composite containing identical fibre fractions by up to a factor of three. In combination, our results show that an asymmetric, systematic variation of fibre properties can successfully combine desirable properties of different fibre types, suggesting new routes for the development of high-performance composites, and improving our understanding of the structure-function relationship of the coconut pericarp.