Diffusion functions in term-structure models are measures of uncertainty about future price movements and are directly related to the risk associated with holding financial securities. Correct specification of diffusion functions is crucial in pricing options and other derivative securities. In contrast to the standard parametric two-factor models, we propose a non-parametric two-factor term-structure model that imposes no restrictions on the functional forms of the diffusion functions. Hence, this model allows for maximum flexibility when fitting diffusion functions into data. A non-parametric procedure is developed for estimating the diffusion functions, based on the discretely sampled observations. The convergence properties and the asymptotic distributions of the proposed non-parametric estimators of the diffusion functions with multivariate dimensions are also obtained. Based on U.S. data, the non-parametric prices of the bonds and bond options are computed and compared with those calculated under an alternative parametric model. The empirical results show that the non-parametric model generates significantly different prices for the derivative securities.