We propose a novel peak-to-average power ratio (PAPR) reduction method based on a peak cancellation (PC) signal vector that considers the variance in the average signal power among transmitter antennas for massive multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) signals using the null space in a MIMO channel. First, we discuss the conditions under which the PC signal vector achieves a sufficient PAPR reduction effect after its projection onto the null space of the MIMO channel. The discussion reveals that the magnitude of the correlation between the PC signal vector before projection and the transmission signal vector should be as low as possible. Based on this observation and the fact that to reduce the PAPR it is helpful to suppress the variation in the transmission signal power among antennas, which may be enhanced by beamforming (BF), we propose a novel method for generating a PC signal vector. The proposed PC signal vector is designed so that the signal power levels of all the transmitter antennas are limited to be between the maximum and minimum power threshold levels at the target timing. The newly introduced feature in the proposed method, i.e., increasing the signal power to be above the minimum power threshold, contributes to suppressing the transmission signal power variance among antennas and to improving the PAPR reduction capability after projecting the PC signal onto the null space in the MIMO channel. This is because the proposed method decreases the magnitude of the correlation between the PC signal vectors before its projection and the transmission signal vectors. Based on computer simulation results, we show that the PAPR reduction performance of the proposed method is improved compared to that for the conventional method and the proposed method reduces the computational complexity compared to that for the conventional method for achieving the same target PAPR.