Mitotic kinesins are essential for faithful chromosome segregation and cell proliferation. Therefore, in humans, kinesin motor proteins have been identified as anti-cancer drug targets and small molecule inhibitors are now tested in clinical studies. Phylogenetic analyses have assigned five of the approximately fifty kinesin motor proteins coded by Trypanosoma brucei genome to the Kinesin-13 family. Kinesins of this family have unusual biochemical properties because they do not transport cargo along microtubules but are able to depolymerise microtubules at their ends, therefore contributing to the regulation of microtubule length. In other eukaryotic genomes sequenced to date, only between one and three Kinesin-13s are present. We have used immunolocalisation, RNAi-mediated protein depletion, biochemical in vitro assays and a mouse model of infection to study the single mitotic Kinesin-13 in T. brucei. Subcellular localisation of all five T. brucei Kinesin-13s revealed distinct distributions, indicating that the expansion of this kinesin family in kinetoplastids is accompanied by functional diversification. Only a single kinesin (TbKif13-1) has a nuclear localisation. Using active, recombinant TbKif13-1 in in vitro assays we experimentally confirm the depolymerising properties of this kinesin. We analyse the biological function of TbKif13-1 by RNAi-mediated protein depletion and show its central role in regulating spindle assembly during mitosis. Absence of the protein leads to abnormally long and bent mitotic spindles, causing chromosome mis-segregation and cell death. RNAi-depletion in a mouse model of infection completely prevents infection with the parasite. Given its essential role in mitosis, proliferation and survival of the parasite and the availability of a simple in vitro activity assay, TbKif13-1 has been identified as an excellent potential drug target.