Doppler suppression techniques with angle-domain Doppler compensation target reducing the time fluctuations of time-varying channel for high-mobility massive MIMO communications. However, the existing Doppler suppression solutions suffer from high peak-to-average power ratio (PAPR). In this letter, we propose a PAPR reduction scheme for Doppler suppression, where an optimization problem is formulated to minimize the Doppler spread under a constraint of tolerable PAPR level. We further develop a suboptimal solution which decomposes the original joint optimization problem into two steps. First, an iterative Fourier technique is employed and the idea of basis expansion model (BEM) is proposed to reduce the computational complexity. Then, the antenna weighting vector is optimized which takes into consideration both Doppler spread and PAPR. Simulation results are provided to demonstrate that the proposed scheme can substantially outperform the existing schemes.