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In this paper, by using the recently compiled set of 120intermediate-luminosity quasars (ILQSO) observed in a single-frequency VLBIsurvey, we propose an improved model-independent method to probe cosmiccurvature parameter $\Omega_k$ and make the first measurement of the cosmiccurvature referring to a distant past, with redshifts up to $z\sim 3.0$.Compared with other methods, the proposed one involving the quasar dataachieves constraints with higher precision in this redshift range. Moreimportantly, our results indicate that the measured $\Omega_k$ is in goodagreement with zero cosmic curvature, implying that there is no significantdeviation from a flat Universe. Finally, we investigate the possibility oftesting $\Omega_k$ with a much higher accuracy using quasars observed in thefuture VLBI surveys. It is shown that our method could provide a reliable andtight constraint on the prior $\Omega_k$ and one can expect the zero cosmiccurvature to be established at the precision of $\Delta\Omega_k\sim 10^{-2}$with 250 well-observed radio quasars.

Milliarcsecond compact structure in radio quasars and the geometry of the universe