  In our previous work \cite{Feng:2013pba}, we have shown a curvaton model
where the curvaton has a nonminimal derivative coupling to gravity. Such a
coupling could bring us scale-invariance of the perturbations for wide range
constant values of the equation-of-state of the cosmic background at the early
time. In this paper, we continue our study by fully analyzing its perturbations
up to the third order. Apart from the usual 2-point correlation function that
has already been calculated in \cite{Feng:2013pba}, we have also taken into
account the 3-point correlation functions including pure scalar part, pure
tensor part, as well as the cross-correlations between scalar and tensor
perturbation modes. We find that for pure scalar part, the 3-point correlation
functions can generate non-Gaussianities that fits the PLANCK data very well.
For pure tensor and mixed parts, the shape functions have peaks at squeezed and
equilateral limits respectively, responsible for sizable $f_{NL}^{sqz}$ and
$f_{NL}^{eql}$, which could be tested by the future observatioanl data.
