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 $1sigma$ 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.
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