  We introduce and investigate a distance-type measure of non-Gaussianity based
on the quantum fidelity. This new measure can readily be evaluated for all pure
states and mixed states that are diagonal in the Fock basis. In particular, for
an $M$-photon added thermal state, an analysis of the Bures degree of
non-Gaussianity is made in comparison with two previous measures built with the
Hilbert-Schmidt metric and the relative entropy. We obtain a compact analytic
formula for the Hilbert-Schmidt non-Gaussianity measure and find a good
consistency of the three examined measures.
