We investigate the peak-to-average power ratio (PAPR) reduction method in downlink massive multi-user multiple-input multiple-output (MIMO)-orthogonal frequency division multiplexing (OFDM) transmission. In this paper, we develop a new complexity-reduced PAPR reduction method based on peak cancellation (PC) signals using the null space in a MIMO channel for MIMO-OFDM signals. The proposed method divides the transmitter antennas jointly considered in the PAPR reduction process and utilizes the low-dimensional null space in the MIMO channel to reduce the computational complexity in the PAPR reduction process. Besides, it can execute PAPR reduction based on PC signals in parallel, suppressing the degradation of PAPR reduction capability due to the reduction of the dimension of the null space in the MIMO channel. Computer simulation results show that the proposed method significantly reduces computational complexity while keeping a sufficient PAPR reduction capability.