To study the bid problem of market-based resource allocation in grid context,an optimal strategy of resource allocation for parallel tasks is presented.Firstly,the problem of multiple users with parallel tasks competing for a common resource is formulated as a max-min problem.Secondly,the principle of maximum entropy is introduced to convert this problem into a differentiable optimal problem.Finally,bisection searching method is used to produce a set of optimal user bids to allocate the resource capacity proportionally.Particularly,the characteristics of the user bid function are studied,and the algorithms for searching ates the optimal solution of the user bid set are given.The results show that the proposed allocation strategy generates low time complexity and improves the efficiency of resource allocation,and thus can satisfy the dynamic nature of the grid environment.