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In this paper, we propose a generative model for full-atom \\textbf{Pep}tide design with \\textbf{G}eometric \\textbf{LA}tent \\textbf{D}iffusion (PepGLAD) given the binding site. We first establish a benchmark consisting of both 1D sequences and 3D structures from Protein Data Bank (PDB) and literature for systematic evaluation. We then identify two major challenges of leveraging current diffusion-based models for peptide design: the full-atom geometry and the variable binding geometry. To tackle the first challenge, PepGLAD derives a variational autoencoder that first encodes full-atom residues of variable size into fixed-dimensional latent representations, and then decodes back to the residue space after conducting the diffusion process in the latent space. For the second issue, PepGLAD explores a receptor-specific affine transformation to convert the 3D coordinates into a shared standard space, enabling better generalization ability across different binding shapes. 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