We propose a new method of instance-level microtubule (MT) tracking in time-lapse image series using recurrent attention. Our novel deep learning algorithm segments individual MTs at each frame. Segmentation results from successive frames are used to assign correspondences among MTs. This ultimately generates a distinct path trajectory for each MT through the frames. Based on these trajectories, we estimate MT velocities. To validate our proposed technique, we conduct experiments using real and simulated data. We use statistics derived from real time-lapse series of MT gliding assays to simulate realistic MT time-lapse image series in our simulated data. This data set is employed as pre-training and hyperparameter optimization for our network before training on the real data. Our experimental results show that the proposed supervised learning algorithm improves the precision for MT instance velocity estimation drastically to 71.3% from the baseline result (29.3%). We also demonstrate how the inclusion of temporal information into our deep network can reduce the false negative rates from 67.8% (baseline) down to 28.7% (proposed). Our findings in this work are expected to help biologists characterize the spatial arrangement of MTs, specifically the effects of MT-MT interactions.