Both parallel and distributed network environment systems play a vital role in the improvement of high performance computing. The primary concern when analyzing these systems is multiprocessor task scheduling. This paper addresses the problem of efficient multiprocessor task scheduling. A multiprocessor task scheduling problem is represented as directed acyclic task graph (DAG), for execution on multiprocessors with communication costs. In this paper we have investigated the effectiveness of a proposed paradigm based on genetic algorithms (GAs). GAs is a class of robust stochastic search algorithms for various combinatorial optimization problems. We have designed a GA based encoding mechanism that uses multi-chromosome encoding scheme. The implementation of the technique is simple. The performance of the designed algorithm has been tested on a variety of multiprocessor systems both heterogeneous as well as homogeneous.