Although most tsunamis are generated by the sea-bottom deformation caused by earthquakes, some tsunamis are excited by sea-surface pressure changes. This study theoretically investigated tsunamis generated by sea-surface pressure changes and derived the solutions in 3-D space, whereas most past studies employed 2-D equations. Using the solutions, we simulated and visualized the tsunami generation by a growing pressure change. Negative pressure change made the sea surface uplifted inside the source region and negative leading waves were radiated from the source region. We also simulated the tsunami generation when the pressure change at the sea surface moves with almost the same speed as the tsunami propagation velocity. The tsunami height increased with increasing the travel distance including the dispersion effects. The 3-D solutions in this study, including the vertical velocity distribution, indicate that both the tsunami height and the sea-surface pressure changes contribute to the ocean-bottom pressure changes, suggesting the difficulty in measuring the tsunami height with ocean-bottom pressure observations. When the pressure change source was characterized by short-wavelength components, the dispersion increased tsunami height more extensively than the non-dispersive tsunamis. The 3-D solutions are necessary for describing the tsunami generation where the long-wave approximations are not applicable in open oceans.