We propose a fair scheduling algorithm for Computational Grids, called Fair Execution Time Estimation (FETE) algorithm. FETE assigns a task to the computation resource that minimizes what we call its fair execution time estimation. The fair execution time of a task on a certain resource is an estimation of the time by which a task will be executed on the resource, assuming it gets a fair share of the resource’s computational power. Though space-shared scheduling is used in practice, the estimates of the fair execution times are obtained assuming that a time-sharing discipline is used. We experimentally evaluate the proposed algorithm and observe that it outperforms other known scheduling algorithms. We also propose a version of FETE, called Simple FETE (SFETE), which requires no a-priori knowledge of the tasks workload and in most cases has similar performance to that of FETE.