Plant organ growth involves significant deformation of cell walls, with the mechanical behavior of these walls, particularly the epidermal cell walls, playing a crucial role in plant morphogenesis. To gain insights into the mechanics of plant growth, it is vital to study and quantify the large-deformation mechanical properties of the epidermal cell walls in the context of development. To this end, we investigated the mechanical response of the Arabidopsis leaf epidermis to stretching. The epidermis exhibited a non-linear stiffening behavior that naturally fell into three regimes. Each regime also corresponded with distinct nonlinear behaviors in terms of transverse deformation (i.e., Poisson effect) and unrecoverable deformation (i.e., plasticity). We found that these properties arise not from the geometric structure of the epidermal cells but rather from the cell wall material, which behaves as a fibrous network material. Using a five-beam model, we demonstrated that these nonlinear behaviors result from the transition from reorientation and bending-dominated to stretch-dominated deformation modes of cellulose microfibrils. We further explored how these mechanical properties change during development and found stiffening behavior is more pronounced at later developmental stage. Finally, our investigation into the spr2-2 mutant with altered morphology shows that it has anisotropic mechanical properties, likely contributing to the leaf curvature. Our finding reveals the fibrous network nature of cell walls, which gives a high degree of tunability in mechanical properties, allowing cells to adjust these properties to support the proper formation of plant organs.