Task assignment problem (TAP) involves assigning a number of tasks to a number of processors in distributed computing systems and its objective is to minimize the sum of the total execution and communication costs, subject to all of the resource constraints. TAP is a combinatorial optimization problem and NP-complete. This paper proposes a hybrid meta-heuristic algorithm for solving TAP in a heterogeneous distributed computing system. To compare our algorithm with previous ones, an extensive computational study on some benchmark problems was conducted. The results obtained from the computational study indicate that the proposed algorithm is a viable and effective approach for the TAP.