We develop a neural parametric model for 3D plant leaves for modeling and reconstruction of plants that are essential for agriculture and computer graphics. While parametric modeling has been actively studied for human and animal shapes, plant leaves present unique challenges due to their diverse shapes and flexible deformation, making common approaches inapplicable. To this problem, we introduce a learning-based parametric model, NeuraLeaf, disentangling the leaves' geometry into their 2D base shapes and 3D deformations. Since the base shapes represent flattened 2D leaves, it allows learning from rich sources of 2D leaf image datasets, and also has the advantage of simultaneously learning texture aligned with the geometry. To model the 3D deformation, we propose a novel skeleton-free skinning model and a newly captured 3D leaf dataset called DeformLeaf. We establish a parametric deformation space by converting the sample-wise skinning parameters into a compact latent representation, allowing for flexible and efficient modeling of leaf deformations. We show that NeuraLeaf successfully generates a wide range of leaf shapes with deformation, resulting in accurate model fitting to 3D observations like depth maps and point clouds. Our implementation and datasets will be released upon acceptance.