Abstract: In this study, the fictitious time integration method (FTIM) is applied to investigate wave propagation over an arbitrary bathymetry with measured uncertainty. The FTIM is used to convert the higher-order elliptic mild-slope equation (EMSE) into a FTIM like EMSE (FTIMEMSE). It has the advantage to describe wave transformation from deep water to shallow water region in a large coastal area with numerical efficiency. The validity of the noise resistance for the measured uncertainty of the bathymetry is also studied. In addition, typical examples for waves propagating over an elliptic shoal rest on a horizontal and sloping bottom is presented. It is concluded that the FTIM is robust in the numerical stability and capable of against the noise of the measurement.