In this paper, we first propose a novel construction of 16-quadrature amplitude modulation (QAM) near-complementary sequences with low peak-to-mean envelope power ratio (PMEPR) in orthogonal frequency division multiplexing (OFDM) systems. The proposed 16-QAM near-complementary sequences can be constructed by utilizing novel nonlinear offsets, where the length of the sequences is n = 2m. The family size of the newly constructed 16-QAM near-complementary sequences is 8 × (m!/2) × 4m+1, and the PMEPR of these sequences is proven to satisfy PMEPR ≤ 2.4. Thus, the proposed construction can generate a number of 16-QAM near-complementary sequences with low PMEPR, resulting in the improvement of the code rate in OFDM systems. Furthermore, we also propose a novel construction of 64-QAM near-complementary sequences with low PMEPR, which is the first proven construction of 64-QAM near-complementary sequences. The PMEPRs of two types of the proposed 64-QAM near-complementary sequences are proven to satisfy that PMEPR ≤ 3.62 or PMEPR ≤ 2.48, respectively. The family size of the newly constructed 64-QAM near-complementary sequences is 64 × (m!/2) × 4m+1.