  In the present work we systematically study $\mathcal{\alpha}$ decay
half-lives of $Z>51$ nuclei using the modified Gamow-like model which includes
the effects of the centrifugal potential and electrostatic shielding. For the
case of even-even nuclei, this model contains two adjustable parameters: the
parameter $a$ related to the screened electrostatic barrier and the radius
constant $r_0$, while for the case of odd-odd and odd-A nuclei, it is added a
new parameter i.e. hindrance factor $h$ which is used to describe the effect of
an odd-proton and/or an odd-neutron. Our calculations can well reproduce the
experimental data. In addition, we use this modified Gamow-like model to
predict the $\mathcal{\alpha}$-decay half-lives of seven even-even nuclei with
$Z=120$ and some un-synthesized nuclei on their $\mathcal{\alpha}$ decay
chains.
