  In this paper, we place constraints on four alternative cosmological models
under the assumption of the spatial flatness of the Universe: CPL, EDE, GCG and
MPC. A new compilation of 120 compact radio quasars observed by
very-long-baseline interferometry, which represents a type of new cosmological
standard rulers, are used to test these cosmological models. Our results show
that the fits on CPL obtained from the quasar sample are well consistent with
those obtained from BAO. For other cosmological models considered, quasars
provide constraints in agreement with those derived with other standard probes
at $1\sigma$ confidence level. Moreover, the results obtained from other
statistical methods including Figure of Merit, $Om(z)$ and statefinder
diagnostics indicate that: (1) Radio quasar standard ruler could provide better
statistical constraints than BAO for all cosmological models considered, which
suggests its potential to act as a powerful complementary probe to BAO and
galaxy clusters. (2) Turning to $Om(z)$ diagnostics, CPL, GCG and EDE models
can not be distinguished from each other at the present epoch. (3) In the
framework of statefinder diagnostics, MPC and EDE will deviate from
$\rm{\Lambda}$CDM model in the near future, while GCG model cannot be
distinguished from $\rm{\Lambda}$CDM model unless much higher precision
observations are available.
