This paper considers the minimization of the makespan for a set of dependent tasks with unit duration and unit communication delays. Given an upper bound of the makespan, release dates and deadlines of the tasks can be computed. Time windows are defined accordingly. We prove that our scheduling problem is fixed-parameter tractable; the parameter is the maximum number of tasks that are schedulable at the same time considering time windows. A fixed-parameter algorithm based on a dynamic programming approach is developed and proved to solve this optimization problem. This is, as far as we know, the first fixed-parameter algorithm for a scheduling problem with communication delays.