The problem of task assignment is one of the most fundamental among combinatorial optimization problems. Solving the Task Assignment Problem is very important for many real time and computational scenarios where a lot of small tasks need to be solved by multiple processors simultaneously. A classic problem that confronts computer scientists across the globe pertaining to the effective assignment of tasks to the various processors of the system due to the intractability of the task assignment problem for more than 3 processors. Several Algorithms and methodologies have been proposed to solve the Task Assignment Problem, most of which use Graph Partitioning and Graph Matching Techniques. Significant research has also been carried out in solving the Task Assignment Problem in a parallel environment. Here we propose a modified version of iterated greedy algorithm that capitalizes on the efficacy of the Parallel Processing paradigm, minimizing the various costs along with the duration of convergence. The central notion of the algorithm is to enhance the quality of assignment in every iteration, utilizing the values from the preceding iterations and at the same time assigning these smaller computations to internal processors (i.e. parallel processing) to hasten the computation. On implementation, the algorithm was tested using Message Passing Interface (MPI) and the results show the effectiveness of the said algorithm.