Taking Rosen-Zener tunneling as the underlying process，a scheme to achieve nonlinear Ramsey interferometry with a two-component trapped Bose-Einstein condensate is proposed. Abundant nonlinear Ramsey interference fringes are observed in time domain by the numerical simulations and these fringes are very different from the sinusoidal pattern for linear Ramsey interference due to the dominant nonlinear interaction between atoms. Furthermore，Fourier transformation results show that the fundamental frequency of Ramsey fringes can exactly reflect the information of nonlinearity or asymmetry. This finding provides an opportunity to measure atomic properties via measuring the frequency of fringes.