This paper presents a new baseband digital predistortion technique, which includes iterative injection of odd-order in-band distortion components, and baseband equalization of the input signal. The former enhances compensation of nonlinearity and gains the optimal ratio of linearization degree to computational complexity by adjusting the number of injections. The latter minimizes memory effects of the power amplifier (PA) using digital signal processing. The proposed linearizer is integrated into the baseband block, and does not require additional radio-frequency components. For demonstration, a wideband 25-dB gain power amplifier is linearized using the proposed predistortion. For a 5-MHz 16-QAM signal the spectral regrowth suppression of 23 dB is achieved.