The current dataset contains Eulerian velocity and pressure fields, and Lagrangian particle trajectories of the wake downstream of a smooth cylinder at a Reynolds number equal to 3900. The open-access Direct Numerical Simulation (DNS) code Incompact3d was used to calculate the Eulerian field around the cylinder. Trajectories of roughly 200,000 particles for two sub-domains are available. This dataset can be used as a test case for tracking algorithm assessment, exploring the physics of Lagrangian particles, statistic analyses, data assimilation and machine learning interests.