The sustainable development of organizations is inseparable from innovation, and tacit knowledge is the core resource used to achieve organizational innovation. Due to the implicitness of tacit knowledge and the complexity of members’ relationships, symbiotic relationships between members have dramatically affected the transfer effect of tacit knowledge. However, previous studies on tacit knowledge transfer only focus on the characteristics of the subject or object; fewer consider the role of symbiotic relationships between knowledge subjects. An organization’s tacit knowledge transfer network (OTKTN) is a dynamic knowledge transfer network established among multiple members. Tacit knowledge transfer and sharing among network members conform to the symbiotic feature. To examine various relationships between members, and to investigate the mechanisms that impact tacit knowledge transfer, this article aims to analyze the symbiotic relationships in OTKTN based on the symbiotic perspective. The Lotka–Volterra model was used to construct symbiotic evolution model, and symbiotic coefficients were constructed from the four levels: knowledge-based psychological personal ownership (KPPO) of the knowledge provider, media richness, trust of the knowledge receiver, and organizational rewards matching, to discuss symbiotic modes. Finally, numerical simulation software was applied to simulate the evolution of knowledge levels in members. The results show that the four kinds of symbiotic modes between members include independence, commensalism, asymmetric mutualism, and symmetric mutualism. Symmetric mutualism is the best mode. In this mode, maximum level in independence mode affects the final stable knowledge level; the initial knowledge amount and natural growth rate both affect knowledge growth rate. Media richness, receiver’s trust, and organizational rewards matching can increase members’ tacit knowledge, but the knowledge provider’s KPPO inhibits members’ tacit knowledge growth. This article provides guidance to form a healthy symbiotic relationship and help organizations increase tacit knowledge.