In this paper, the precoding-based peak-to-average power ratio (PAPR) reduction methods are studied for the massive multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) system in the angular domain. The expectation maximization generalized approximate message passing algorithm and the proposed optimized alternating direction method of multipliers (OADMM) scheme are adopted here to explore the system characteristics in terms of the symbol error ratio (SER) performance, the PAPR reduction efficiency, and the inter user interference (IUI). Specifically, the high PAPR problem is reduced to no more than 0.18 dB by using the inherent property of the massive MIMO-OFDM angle division multiple access (ADMA) system with relatively reduced computational complexity. Moreover, the value of SER is around 10−5 dB when the proposed technique is performed. Computer numerical simulation results verify the efficiency of the proposed technique from the perspective of SER, PAPR suppression, and IUI.