Milliarcsecond-scale observations of high-redshift radio quasars provide unique insight to jet structure, formation and evolution. To date, only a handful of already known high-redshift ($z>4$) radio quasars had been imaged with very long baseline interferometry (VLBI). To substantially increase the sample available for studying the population of high-redshift radio-loud active galactic nuclei, we selected 13 radio quasars for imaging with the European VLBI Network (EVN) at 1.7 and 5 GHz. Here we present the preliminary analysis of the experiment lasting for almost three years, by investigating the spectral characteristics, morphology and brightness temperature of the sources. Compact radio emission was detected in all objects. Our results indicate that about half of the sample consists of unbeamed radio sources, some of which show significant offset between the optical and radio positions.