Will-be-set-by-IN-TECH computing resources and have to submit their service request at just one point of entry to the grid system.Foster introduced the concept of Virtual Organization (VO) (Foster et al., 2001).He defines VO as a "dynamic collection of multiple organizations providing flexible, secure, coordinated resource sharing".Figure 1 shows three actual organizations with both computational and data resources to share across organizational boundaries.Moreover, the same figure forms two VOs, A and B, each of them can have access to a subset of resources in each of the organizations (Moallem, 2009).Virtualization is a mechanism that improves the usability of grid computing systems by providing environment customization to users.2. Heterogeneity: The organizations that form part of VO may have different resources such as hardware, operating system and network bandwidth.Accordingly, VO is considered as a collection of heterogeneous resources of organizations.3. Dynamism: In the grid system, organizations or their resources can join or leave VO depending on their requirements or functional status.Grid systems provide the ability to perform higher throughput computing by usage of many networked computers to distribute process execution across a parallel infrastructure.Nowadays, organizations around the world are utilizing grid computing in such diverse areas as collaborative scientific research, drug discovery, financial risk analysis, product design and 3-D seismic imaging in the oil and gas industry (Dimitri et al., 2005).Interestingly, task scheduling in grid has been paid a lot of attention over the past few years.The important goal of task scheduling is to efficiently allocate tasks as fast as possible to avialable resources in a global, heterogeneous and dynamic environment.Kousalya pointed out that the grid scheduling consists of three stages: First, resource discovery and filtering.Second, resource selection and scheduling according to certain objective.Third, task submission.The third stage includes the file staging and cleanup (Kousalya & Balasubramanie, 2009; 2008).High performance computing and high throughput computing are the two different goals of grid scheduling algorithm.The main aim of the high performance computing is to minimize the execution time of the application.Allocation of resources to a large number of tasks in grid computing environment presents more difficulty than in conventional computational environments.The scheduling problem is well known NP-complete (Garey & Johnson, 1979).It is a combinatorial optimization problem by nature.Many algorithms are proposed for task scheduling in grid environments.In general, the existing heuristic mapping can be divided into two categories (Jinquan et al., 2005):First, online mode, where the scheduler is always in ready mode.Whenever a new task arrives to the scheduler, it is immediately allocated to one of the existing resources required by that task.Each task is considered only once for matching and scheduling.Second, batch mode, the tasks and resources are collected and mapped at prescheduled time.This mode takes better decision because the scheduler knows the full details of the available tasks and resources.This chapter proposes a heuristic algorithm that falls in batch mode Jinquan et al. ( 2005).However, this chapter studies the problem of minimizing makespan, i.e., the total execution time of the schedule in grid environment.The proposed Mutation-based Simulated Annealing (MSA) algorithm is proved to have high performance computing scheduling algorithm.MSA algorithm will be studied for random and Expected Time to Compute (ETC) Models.