A barrier option is a kind of path-dependent option whose return depends on whether the price of the underlying asset reaches a certain barrier level. This paper mainly analyzes European barrier option pricing formulas for the uncertain exponential Ornstein–Uhlenbeck model with a floating interest rate. The corresponding numerical algorithms for the knock-in and knock-out option prices are designed. Several numerical examples are given to study the relationship between barrier option prices and parameters. Finally, a real-data example is presented to illustrate the option pricing formulas.