As we know, harmonic noises widely exist in industrial fields and have a crucial impact on the computational accuracy of the zeroing neural network (ZNN) model. For tackling this issue, by combining the dynamics of harmonic signals, two harmonic noise-tolerant ZNN (HNTZNN) models are designed for the dynamic matrix pseudoinversion. In the design of HNTZNN models, an adaptive compensation term is adopted to eliminate the influence of harmonic noises, and a Li activation function is introduced to further improve the convergence rate. The convergence and robustness to harmonic noises of the proposed HNTZNN models are proved through theoretical analyses. Besides, compared with the ZNN model without adaptive compensation term, the HNTZNN models are more effective for tacking the problem of dynamic matrix pseudoinverse under harmonic noises environments. Moreover, HNTZNN models are further applied to the kinematic control of a four-link planar robot manipulator under harmonic noises. In general, the experimental results verify the effectiveness, superiority, and broad application prospect of the models.