Understanding human fertility requires dynamic and three-dimensional (3D) analysis of sperm movement, which extends beyond the capabilities of traditional datasets focused primarily on two-dimensional sperm motility or static morphological characteristics. To address this limitation, we introduce the 3D+t Multifocal Imaging Dataset of Human Sperm (3D-SpermVid), a repository comprising 121 multifocal video-microscopy hyperstacks of freely swimming sperm cells, incubated under non-capacitating conditions (NCC) and capacitating conditions (CC). This collection enables detailed observation and analysis of 3D sperm flagellar motility patterns over time, offering novel insights into the capacitation process and its implications for fertility. Data were captured using a multifocal imaging (MFI) system based on an optical microscope equipped with a piezoelectric device that adjusts focus at various heights, recording sperm movement in a volumetric space. By making this data publicly available, we aim to enable applications in deep learning and pattern recognition to uncover hidden flagellar motility patterns, fostering significant advancements in understanding 3D sperm morphology and dynamics, and developing new diagnostic tools for assessing male fertility, as well as assisting in the self-organizaton mechanisms driving spontaneous motility and navigation in 3D.