Task scheduling is an integrated component of computing. With the emergence of Grid and ubiquitous computing, new challenges appear in task scheduling based on properties such as security, quality of service, and lack of central control within distributed administrative domains. A Grid task scheduling framework must be able to deal with these issues. One of the goals of Grid task scheduling is to achieve high system throughput while matching applications with the available computing resources. This matching of resources in a non-deterministically shared heterogeneous environment leads to concs over Quality of Service (QoS). In this paper a novel QoS guided task scheduling algorithm for Grid computing is introduced. The proposed novel algorithm is based on a general adaptive scheduling heuristics that includes QoS guidance.The algorithm is evaluated within a simulated Grid environment. The experimental results show that the new QoS guided Min-Min heuristic can lead to significant performance gain for a variety of applications. The approach is compared with others based on the quality of the prediction formulated by inaccurate information.