In this paper, the authors study totally real 2-harmonic submanifolds in a Quaternion Projective Space by means of moving frames, we obtain a promotion of Simons＇ type integral inequality of compact sub- manifolds as well as some pinching tbeorems.%利用了活动标架法对四元射影空间QPnc中全实2-调和子流形进行了研究，获得了这类子流形成为全实极小子流形的刚性定理，推广了相关文献中的积分不等式．
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