Provided are a computer program product, system, and method for determining cores to assign to cache hostile tasks. A computer system has a plurality of cores. Each core is comprised of a plurality of processing units and at least one cache memory shared by the processing units on the core to cache data from a memory. A task is processed to determine one of the cores on which to dispatch the task. A determination is made as to whether the processed task is classified as cache hostile. A task is classified as cache hostile when the task accesses more than a threshold number of memory address ranges in the memory. The processed task is dispatched to at least one of the cores assigned to process cache hostile tasks.