Large Language Models (LLMs) excel in network algorithm design but suffer from inefficient iterative coding and high computational costs. Drawing inspiration from butterfly metamorphosis—where structured developmental phases (Phase I: larval nutrient accumulation → Phase II: pupal transformation) enable adaptive evolution—we propose Nested-Refinement Metamorphosis (NeRM). Building on this principle, we introduce Metamorphosis on Prompts (MoP) to iteratively refine task descriptions (e.g. latency / bandwidth constraints) and Metamorphosis on Algorithms (MoA) to generate more effective solutions (e.g. appropriate network processing architecture). Their nested refinement ensures task-algorithm alignment, systematically improving both task descriptions and algorithmic solutions for more efficient algorithm design. To further enhance efficiency, we incorporate predictor-assisted code evaluation, mimicking natural selection by filtering out weak candidates early and reducing computational costs. Experimental results on TSP (routing), MKP (resource allocation), and CVRP (service-network coordination) demonstrate that NeRM consistently outperforms state-of-the-art approaches in both performance and efficiency.