When a subduction-zone earthquake occurs, the tsunami height must be predicted to cope with the damage generated by the tsunami. Therefore, tsunami height prediction methods have been studied using simulation data acquired by large-scale calculations. In this research, we consider the existence of a nonlinear power law relationship between the water pressure gauge data observed by the Dense Oceanfloor Network System for Earthquakes and Tsunamis (DONET) and the coastal tsunami height. Using this relationship, we propose a nonlinear parametric model and conduct a prediction experiment to compare the accuracy of the proposed method with those of previous methods and implement particular improvements to the extrapolation accuracy.