A quasi-Newton waveform relaxation (WR) algorithm for semi-linear reaction-diffusion equations is presented at first in this paper.Using the idea of energy estimate,a general proof method for convergence of the continuous case and the discrete case of quasi-Newton WR is given,which appears to be the superlinear rate.The semi-linear wave equation and semi-linear coupled equations can similarly be solved by quasi-Newton WR algorithm and be proved as convergent with the energy inequalities.Finally several parallel numerical experiments are implemented to confirm the effectiveness of the above theories.