The nonlinear phenomena of high-density cylindrical Bose-Einstein condensates caused by atomic interactions in their interference process are studied by using the time-dependent Gross-Pitaevskii equation. It is found that the density structure of one-dimensional interference fringes of Bose-Einstein condensates is in form of a standing wave. Through the nonlinear coupling interactions between atomic waves, the structure appears as the matter-wave gratings, and diffracts its surrounding atomic waves.