  In this paper we investigate the medium modifications of girth distributions
for inclusive jets and $Z^0$ tagged jets with small radius ($R=0.2$) in Pb+Pb
collisions with $\sqrt{s}=2.76$ TeV at the LHC. The partonic spectrum in the
initial hard scattering of elementary collisions are obtained by a event
generator POWHEG+PYTHIA, which matches the next-to-leading (NLO) matrix
elements with parton showering, and energy loss of faster parton traversing in
hot/dense QCD medium is calculated by Monte Carlo simulation within
Higher-Twist formalism of jet quenching in heavy-ion collisions. We present the
model calculations of event normalized girth distributions for inclusive jets
in p+p and Pb+Pb collisions at $\sqrt{s}=2.76$ TeV, which give nice
descriptions of ALICE measurements. It is shown that the girth distributions of
inclusive jets in Pb+Pb are shifted to lower girth region relative to that in
p+p. Thus the nuclear modification factor of girth distributions for inclusive
jets is larger than unity at small girth region, while smaller than one at
large girth region. This behavior results from more soft fragments inside a jet
as well as the fraction alteration of gluon/quark initiated jets in heavy-ion
collisions. We further predict the girth distributions for $Z^0$ boson tagged
jets in Pb+Pb collisions at $\sqrt{s}=2.76$ TeV, and demonstrate that the
medium modification on girth distributions for $Z^0$ tagged jets is less
pronounced as compared to that for inclusive jets because the dominant
components of $Z^0$ tagged jets are quark-initiated jets.
