This paper constructs a relationship lending model, which considers the banker's optimal default decision as a real option, for agents with time-inconsistent preferences. The numerical results indicate that the inconsistency of time preferences induces an earlier default choice for the lender, and leads to a higher financing cost for the borrower. As a result, the values of the projects of banker and entrepreneur with time-inconsistent preferences suffer substantially. Moreover, the comparison between naive agents and mature agents shows that naive agents enjoy a bliss that their false belief can curb the increase of default risk due to the inconsistency, and reduce the optimal relationship rents for enterprises with financial constraints. The model constructed in this paper not only enriches the theoretical research related to relationship lending, but also points out that the optimal relationship rent (financing cost) is higher under the condition that agents have inconsistent time preferences, which provides a new explanation for the dilemma of expensive financing for SMEs from the perspective of time preferences.