The rapid advancement of large language models (LLMs) has transformed the landscape of agentic information seeking capabilities through the integration of tools such as search engines and web browsers. However, current mainstream approaches for enabling LLM web search proficiency face significant challenges: supervised fine-tuning struggles with data production in open-search domains, while RL converges quickly, limiting their data utilization efficiency. To address these issues, we propose EvolveSearch, a novel iterative self-evolution framework that combines SFT and RL to enhance agentic web search capabilities without any external human-annotated reasoning data. Extensive experiments on seven multi-hop question-answering (MHQA) benchmarks demonstrate that EvolveSearch consistently improves performance across iterations, ultimately achieving an average improvement of 4.7\% over the current state-of-the-art across seven benchmarks, opening the door to self-evolution agentic capabilities in open web search domains.