Large Language Models (LLM) technology is rapidly advancing towards human- like dialogue. Values are fundamental drivers of human behavior, yet research on the values expressed in LLM-generated text remains limited. While prior work has begun to explore value ranking in LLMs, the crucial aspect of value correlation – the interrelationship and consistency between different values – has been largely un-examined. Drawing on established psychological theories of human value structure, this paper investigates whether LLMs exhibit human-like value correlations within a single session, reflecting a coherent “persona”. Our findings reveal that standard prompting methods fail to produce human-consistent value correlations. However, we demonstrate that a novel prompting strategy (referred to as "Value Anchoring"), significantly improves the alignment of LLM value correlations with human data. Furthermore, we analyze the mechanism by which Value Anchoring achieves this effect. These results not only deepen our understanding of value representation in LLMs but also introduce new methodologies for evaluating consistency and human-likeness in LLM responses, highlighting the importance of explicit value prompting for generating human-aligned outputs.