Antimicrobial peptide (AMP) is a promising therapy in the treatment of broad-spectrum antibiotics and drug-resistant infections. Recently, an increasing number of researchers have been introducing deep generative models to accelerate AMP discovery. However, current studies mainly focus on sequence attributes and ignore structure information, which is important in AMP biological functions. In this paper, we propose a latent sequence-structure model for AMPs (LSSAMP) with multi-scale VQ-VAE to incorporate secondary structures. By sampling in the latent space, LSSAMP can simultaneously generate peptides with ideal sequence attributes and secondary structures. Experimental results show that the peptides generated by LSSAMP have a high probability of AMP, and two of the 21 candidates have been verified to have good antimicrobial activity. Our model will be released to help create high-quality AMP candidates for follow-up biological experiments and accelerate the whole AMP discovery.