Screenings of the quark-gluon plasma in electric and magnetic sectors are studied on the basis of generalized Polyakov-line correlation functions in lattice QCD simulations with two flavors of improved Wilson quarks. Using the Euclidean-time reflection (R) and the charge conjugation (C), electric and magnetic screening masses are extracted in a gauge-invariant manner. Long distance behavior of the standard Polyakov-line correlation in the quark-gluon plasma is found to be dictated by the magnetic screening. Also, the ratio of the two screening masses agrees with that obtained from the dimensionally-reduced effective field theory and the N = 4 supersymmetric Yang-Mills theory.