A new scheme combining a Lee-Goldburg (LG) sequence with frequency modulation is proposed for cross-polarization (LG-FMCP) in solid-state magic-angle-spinning nuclear magnetic resonance. During the CP contact time, the (1)H magnetization is spin-locked along the magic angle by the LG sequence and the irradiation offset of the S spins (e.g., (15)N) is modulated sinusoidally with a constant RF amplitude. It is shown experimentally that the LG sequence significantly lengthens the proton spin-lattice relaxation time in the tilted rotating frame and that the frequency modulation shortens the cross-polarization time for non-protonated S spins. As a result of substantially increasing the difference in these relaxation rates, the non-protonated and protonated S spins can be more efficiently and more uniformly polarized with a relatively long CP contact time, making quantitative CP measurements possible. A sample of (15)N-delta 1-L-histidine lyophilized from a solution of pH 6.3 and a (15)N-delta 1-L-His labeled transmembrane helical peptide in hydrated lipid bilayers were used to illustrate the advantages of this scheme.