We investigate the peak-to-average power ratio (PAPR) reduction problem in orthogonal frequency-division multiplexing (OFDM) based massive multiuser (MU) multiple-input multiple-output (MIMO) downlink systems. In this paper, we develop a downlink transmission scheme that performs jointly MU precoding and PAPR reduction (PP) by exploiting the excess degrees of freedom (DoF) offered by equipping the BS by a large number of antennas. Specifically, the joint MU precoding and PAPR reduction scheme is formulated as a simple convex optimization problem solved via steepest gradient descent (GD) approach. Then, we develop a novel algorithm, referred to as MU-PP-GDm, to reduce the PAPR of the transmitted signals by exploiting the high-dimensional null-space of the MIMO channel matrix while maintaining excellent transmission quality. Simulation results show that the proposed MU-PP-GDm has a low computational complexity and can achieve substantial PAPR performance with fast convergence rate. INDEX TERMS 5G+, massive multiple-input multiple-output (MIMO), orthogonal frequency-division multiplexing (OFDM), peak-to-average power ratio (PAPR), multiuser (MU) precoding, convex optimization , gradient descent (GD).