Using amino acid residues in peptide generation has solved several key problems, including precise control of amino acid sequence order, customized peptides for property modification, and large-scale peptide synthesis. Proteins contain unknown amino acid residues. Extracting them for the synthesis of drug-like peptides can create novel structures with unique properties, driving drug development. Computer-aided design of novel peptide drug molecules can solve the high-cost and low-efficiency problems in the traditional drug discovery process. Previous studies faced limitations in enhancing the bioactivity and drug-likeness of polypeptide drugs due to less emphasis on the connection relationships in amino acid structures. Thus, we proposed a reinforcement learning-driven generation model based on graph attention mechanisms for peptide generation. By harnessing the advantages of graph attention mechanisms, this model effectively captured the connectivity structures between amino acid residues in peptides. Simultaneously, leveraging reinforcement learning's strength in guiding optimal sequence searches provided a novel approach to peptide design and optimization. This model introduces an actor-critic framework with real-time feedback loops to achieve dynamic balance between attributes, which can customize the generation of multiple peptides for specific targets and enhance the affinity between peptides and targets. Experimental results demonstrate that the generated drug-like peptides meet specified absorption, distribution, metabolism, excretion, and toxicity properties and bioactivity with a success rate of over 90$\%$, thereby significantly accelerating the process of drug-like peptide generation.