Pore-pressure estimation is an important part of oil-well drilling because drilling into unexpected highly pressured fluids can be costly and dangerous. However, standard estimation methods rarely account for the many sources of uncertainty, or for the multivariate nature of the system. We have developed the pore-pressure sequential dynamic Bayesian network (PP SDBN) as an appropriate solution to both these issues. The PP SDBN models the relationships between quantities in the pore-pressure system, such as pressures, porosity, lithology, and wireline-log data, using conditional probability distributions based on geophysical relationships to capture our uncertainty about these variables and the relationships between them. When wireline log data are given to the PP SDBN, the probability distributions are updated, providing an estimate of pore pressure along with a probabilistic measure of uncertainty that reflects the data acquired and our understanding of the system. This is the advantage of a Bayesian approach. Our model provides a coherent statistical framework for modeling the pore-pressure system. The specific geophysical relationships used can be changed to better suit a particular setting, or reflect geoscientists’ knowledge. We determine the PP SDBN on an offshore well from West Africa. We also perform a sensitivity analysis, demonstrating how this can be used to better understand the working of the model and which parameters are the most influential. The dynamic nature of the model makes it suitable for real-time estimation during logging while drilling. The PP SDBN models the shale pore pressure in shale-rich formations with mechanical compaction as the overriding source of overpressure. The PP SDBN improves on existing methods because it produces a probabilistic estimate that reflects the many sources of uncertainty present.