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Sommerfeld enhancement is a generic phenomenon which occurs when slowly moving heavy(compared to mediating particle mass) particles annihilate, and also plays an important role for annihilation of slowly moving particles in thermal environment. In this enhancement, bound states have a significant effect since bound states increase the probability for the encounter. In thermal environment, various thermal effect can have O(1) effect on bound states and bound states may disappear. Thus non-perturbative and non-linear calculation of thermal Sommerfeld factor is necessary. Here we discuss our calculation of the thermal averaged Sommerfeld factor for the annihilation process of heavy quark and heavy anti-quark in Quark-Gluon Plasma(QGP) using lattice version of NRQCD and compare the factor using "Schrodinger equation method". We found that O(100) increase in the thermally averaged Sommerfeld factor for S-wave quarkonium annihilation. We attribute that such increase is due to the bound state effect. In addition, we found that similar (to heavy quark annihilation in QGP) consideraton can be given for various dark matter annihilation scenarios in cosmological context.