Recent advancements in Large Language Models (LLMs) have exhibited notable efficacy in natural language processing (NLP) tasks across diverse domains. Their prowess in integrating extensive knowledge has fueled interest in developing LLM-based autonomous agents. Furthermore, in the realm of finance, there is a persistent need to develop automated systems capable of transforming vast quantities of real-time data into executable decisions, while fully understanding the critical timing of various types of information. LLM agents with rational architecture, compared with their Deep Reinforcement Learning (DRL) counterparts, exceed in their ability to integrate textual data and interpretability in their decision-making process. We introduce FinMem, a novel LLM-based agent framework devised for financial trading. It encompasses three core modules: Profiling, to customize the agent's characteristics; Memory, with layered message processing, to aid the agent in assimilating hierarchical financial data; and Decision-making, to convert insights gained from memories into investment decisions. Notably, FinMem's memory module aligns closely with the cognitive structure of human traders, offering robust interpretability and real-time tuning. Its adjustable cognitive span allows for the retention of critical information beyond human perceptual limits, thereby enhancing trading outcomes. This framework enables the agent to self-evolve its professional knowledge, react agilely to new investment cues, and continuously refine trading decisions in the volatile financial environment. We first compare FinMem with various algorithmic agents on a scalable real-world financial dataset, underscoring its leading trading performance in stocks. We then fine-tuned the agent's perceptual span and character setting to achieve a significantly enhanced trading performance. Collectively, FinMem presents a cutting-edge LLM agent framework for automated trading, boosting cumulative investment returns.