The analytical convolution solution of 1-D fully nonlinear shallow water equations derived by Carrier et al. (2003) is applied to estimate the maximum wave height and the inundation distance during the 2004 Indian Ocean Tsunami. The applied area is in the east coast of Sri Lanka with latitude between 6.8°N and 8°N. The offshore condition for the wave form and vertically-averaged flow velocity are obtained by solving the linear version of the COMCOT tsunami model and has been verified by comparing with the record at Maldives. By taking the nearshore shelf slope as the constant bottom slope for the analytical solution, the inundation distance in the applied area is between 500m and 2.75 km, and the maximum wave height is between 4.46m and 6.63m. The max tsunami height calculated by the present method agrees very well with the in-situ measurement. Therefore, this method is a very useful tool for tsunami early warning by quickly estimating if the max wave height is higher than the seawall or the breakwater. The max inundation distance calculated by the analytic convolution solution also has reasonable agreement with the field survey, but the value of the in-situ investigation scatters widely which suggests the detailed local topography play an important role. Different method for the determination of the bottom slope is also tested and the result show that the slope should be based on the bathymetry nearshore.