We use the X-ray luminosity relation of radio-loud quasars (RLQs) to measure these luminosity distances as well as estimate cosmological parameters. We adopt four parametric models of X-ray luminosity to test luminosity correlation for RLQs and radio-intermediate quasars (RIQs) and give these cosmological distances. By Bayesian information criterion (BIC), the data suggest that the luminosity relation L_X_{prop.to}L_UV_^gamma-uv^L_Radio_^gamma-radio^ for RLQs has better goodness of fit, relative to other models, which can be interpreted as this relation being preferred for RLQs. Meanwhile, we compare the results from flat-spectrum radio-loud quasars (FSRLQs) and steep-spectrum radio-loud quasars (SSRLQs), which indicate that their luminosity correlations are not exactly the same. We also consider dividing the RLQs sample into various redshift bins, which can be used to check if the X-ray luminosity relation depends on the redshift. Finally, we apply a combination of RLQs and SNla Pantheon to verify the nature of dark energy concerning.