To better capture the long-term memory, non-stationary increments, self-similarity, and stochastic nature of interest rates in financial markets, we introduce the Vasicek stochastic interest rate model within a mixed sub-fractional Brownian motion framework to study European option pricing. Using actuarial pricing methods, we derived a closed-form solution for European options under this model. Through numerical simulations and empirical analysis, we examined how variables such as the underlying asset's initial price, strike price, maturity time, volatility, Hurst index, and correlation coefficients influence option prices.