Offshore real-time ocean bottom networks of seismometers and ocean bottom pressure (OBP) gauges have been recently established such as DONET and S-net around the Japanese islands. One of their purposes is to practice rapid and accurate tsunami forecasting. Near-fault OBP records, however, are always contaminated by nontsunami components such as sea-bottom acceleration change until an earthquake stops its fault or sea-floor motions. This study proposes a new method to separate tsunami and ocean bottom displacement components from coseismic OBP records in a real-time basis. Associated with the Off-Mie earthquake of 2016 April 1, we first compared OBP data with acceleration, velocity, and displacement seismograms recorded by seismometers at common ocean bottom sites in both time and frequency domains. Based on this comparison, we adopted a band-pass filter of 0.05–0.15 Hz to remove ocean-bottom acceleration components from the OBP data. Resulting OBP waveforms agree well with the tsunami components estimated by a 100-s low-pass filter with records of several hundred seconds in length. Our method requires only an early portion of a given OBP record after 30 s of an origin time in order to estimate its tsunami component accurately. Our method enhances early tsunami detections with near-fault OBP data; that is, it will make a tsunami forecasting system faster and more reliable than the previous detection schemes that require data away from source regions or after coseismic motions are over.