Earthquakes often occur and may induce the ionospheric disturbance. In order to understand the generation and process of the earthquake, the seismic ionospheric disturbance (SID) may provide insights on earthquakes. In this paper, the seismic ionospheric disturbances following the Mw 7.7 Jamaica earthquake on 28 January 2020 are detected after 12min of the main shock by the dual-frequency GPS measurements. Two disturbances in different azimuths are significantly found by satellite PRN26 and PRN03. The one is located at the southwest area in the range of 700-800km away from the epicenter while the other is located at the southeast area in the range of 200-450km. The propagation speeds of the two disturbances are 2.53km/s and 2.57km/s respectively. Furthermore, we estimated the detailed characteristics of SID (primarily the amplitude, elevation and azimuth angle, waveform and frequency) and discussed the generation and motion process of the ionospheric disturbance with seismograph, focal mechanism and magnetic field. The relation among SID, Rayleigh wave and focal mechanism are interpreted. Furthermore, the azimuthal asymmetry of SID amplitude and the appearance of the inverted N-shape waveform observed by satellite PRN26 are the main distinctions in the two disturbances as a result. Finally, the up propagating secondary acoustic wave triggered by the seismic Rayleigh wave from the strike-slip earthquake is the main source of the two disturbances.