Precision　matrix　(inverse　covariance　matrix)　estimation　is　a　rising　challenge　in　contemporary　applications　while　dealing　with　high-dimensional　data.　This　paper　focuses　on　large-scale　precision　matrix　of　the　random　vector　that　only　has　lower　polynomial　moments.　We　mainly　investigate　upper　bounds　of　the　proposed　estimator　under　the　spectral　norm　in　terms　of　the　probability　and　mean　estimation　respectively.　It　is　shown　that　the　data-driven　estimator　is　fully　adaptive　and　achieves　the　same　optimal　convergence　order　as　under　Gaussian　assumption　on　the　data.　Simulation　studies　further　support　our　theoretical　claims.