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Because of inevitable coupling with the environment,nearly all practical quantum systems are opensystems,where the evolution is not necessarily unitary.We proposed an efficient quantum algorithm forsimulating Hamiltonian in an open quantum system on a duality quantum computer.In the algorithm,the timeevolution of open quantum system is realized by using Kraus operators which is naturally realized in dualityquantum computing.The query complexity of the algorithm is reduced from d^4 to d^3,where d is thedimension of the open quantum system.The duality quantum algorithm provides an exponential improvementin precision than Lloyds algorithm because of use of a truncated Taylor series of evolution operators.