Abstract: In this paper, we present a speculative simulated annealing algorithm for taskmapping. Speculative computing is introduced into simulated annealing to solve the taskmapping problem. The concept of task graph and cost function are introduced. The algorithm not only takes computing time of a task into account, but also deals with communicating time. It maintains the serial sequence that the simulated annealing requires,and converges to a global optimum solution. And at the same time, it speeds up the solution and improves parallel computing efficiency.