We apply the inverse-Gaussianization method proposed in citealt{arXiv:1607.05007} to fast produce weak lensing convergence maps and investigate the peak statistics, including the peak height counts and peak steepness counts, in these mocks. We find that the distribution of peak height and steepness is in good agreement with the simulation. The difference is $lesssim 20%$ for these peak statistics in the maps at source redshift $z_s=1$. Besides, the loss of off-diagonal elements in peak covariance motivates us to consider the super sample variance in weak lensing peak statistics. We propose correction methods to effectively recover the (anti-)correlation among different bins by adding scatters in the mean value of these mocks. Finally, as an example of the application, we adopt the improved inverse-Gaussianization method with the above improvement to fast generate 40,000 mocks to calculate precision matrices between the power spectrum and peak statistics.
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