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As one of attractive techniques, partial transmit sequence (PTS) provides an effective solution for peak-to-average power ratio (PAPR) reduction of orthogonal frequency division multiplexing (OFDM) signals. However, optimal PTS (O-PTS) requires an exhaustive search over all combinations of allowed phase weighting factors, resulting in large computational complexity. In this paper, two phase weighting methods with low computational complexity for PTS, named grouping phase weighting (GPW) and recursive phase weighting (RPW), are proposed. These two methods focus on simplifying the computation for candidate sequences and obtaining the same candidate sequences compared to O-PTS. Moreover, the combination of two phase weighting methods can obtain further computational complexity reduction. Theoretical analysis and simulation results show that, compared with O-PTS, PTS employing GPW or/and RPW can not only dramatically reduce computational complexity but also have an advantage of no loss in PAPR reduction performance.