Does central limit theorem work well for Pareto distribution?
One key assumption of the central limit theorem is that the variance $\sigma^2$ of the underlying distribution is finite.  I would guess that you are using a parameterization of the Pareto for which $\sigma^2 = \infty$, in which case the CLT will not hold.  If you tweak your scale parameter so that $\sigma^2 &lt; \infty$ you should see the result you want.