Large language models (LLMs) have shown remarkable progress in code generation, but their generated code often suffers from inefficiency, resulting in longer execution times and higher memory consumption. To address this issue, we propose \textbf{S}elf \textbf{O}ptimization based on Overhe\textbf{A}d \textbf{P}rofile (\textbf{SOAP}), a self-optimization framework that utilizes execution overhead profiles to improve the efficiency of LLM-generated code. SOAP first generates code using an LLM, then executes it locally to capture execution time and memory usage profiles. These profiles are fed back to the LLM, which then revises the code to reduce overhead. To evaluate the effectiveness of SOAP, we conduct extensive experiments on EffiBench and two commonly used code generation benchmarks with 16 open-source and 6 closed-source models. Our evaluation results demonstrate that through iterative self-optimization, SOAP significantly enhances the efficiency of LLM-generated code. For example, the execution time (ET) of StarCoder2-15B for the EffiBench decreases from 0.93 (s) to 0.12 (s) which reduces 87.1\% execution time requirement compared with the initial code. The total memory usage (TMU) of StarCoder2-15B also decreases from 22.02 (Mbs) to 2.03 (Mbs), which decreases 90.8\% total memory consumption during the execution process.