This paper presents an approach for the detection of early weak Tsunami in presence of large noise in sea surface height (SSH) measurements obtained such as using a satellite-carried global navigation satellite system (GNSS) receiver and the GNSS reflectometry (GNSS-R) technique. A sliding window moving average (SWMA) technique is proposed for detecting a Tsunami lead wave and a hypothesis testing method is developed to decide whether or not a Tsunami is present by examining the SWMA outputs against a predefined threshold. The proposed approach is evaluated using the 2011 Japan's Tsunami data collected by altimetry satellite Jason-1. Simulation results demonstrate that the proposed detect method considerably outperforms the existing methods.