Efficient task scheduling is essential for obtaining high performance in heterogeneous distributed computing systems (or HeDCSs). Because of its key importance, several scheduling algorithms have been proposed in the literature, which are mainly for homogeneous processors. Few scheduling algorithms are developed for HeDCSs. In this paper, we present a novel task scheduling algorithm, called the Longest Dynamic Critical Path (LDCP) Algorithm, for HeDCSs. The LDCP algorithm is a list-based scheduling algorithm that uses a new attribute to effectively compute the priorities of tasks in HeDCSs. At each scheduling step, the LDCP algorithm selects the task with the highest priority and assigns the selected task to the processor that minimizes its finish execution time using an insertion-based scheduling policy. The LDCP algorithm successfully generates task schedules that outperform, to the best of our knowledge, two of the best scheduling algorithms for HeDCSs.