A new method was developed to reproduce the tsunami height distribution in and around the source area, at a certain time, from a large number of ocean bottom pressure sensors, without information on an earthquake source. A dense cabled observation network called S-NET, which consists of 150 ocean bottom pressure sensors, was installed recently along a wide portion of the seafloor off Kanto, Tohoku, and Hokkaido in Japan. However, in the source area, the ocean bottom pressure sensors cannot observe directly an initial ocean surface displacement. Therefore, we developed the new method. The method was tested and functioned well for a synthetic tsunami from a simple rectangular fault with an ocean bottom pressure sensor network using 10 arc-min, or 20 km, intervals. For a test case that is more realistic, ocean bottom pressure sensors with 15 arc-min intervals along the north-south direction and sensors with 30 arc-min intervals along the east-west direction were used. In the test case, the method also functioned well enough to reproduce the tsunami height field in general. These results indicated that the method could be used for tsunami early warning by estimating the tsunami height field just after a great earthquake without the need for earthquake source information.