Cyanoacetylene, HCC-CN is a ubiquitous molecule in the Universe. However, its interstellar chemistry is not well understood and its understanding requires laboratory data including rotational spectroscopy of possible products coming from a reaction with another compounds. In this study we present the first spectroscopic characterization of gauche conformation of 4-hydroxy-2-butynenitrile (HOCH2CCCN), a formal adduct of cyanoacetylene on formaldehyde, in the frequency range up to 500 GHz. The analysis of the rotational spectrum was complicated by internal rotation of the OH group that connects two equivalent gauche configurations. The spectral assignment was aided by high-level quantum chemical calculations that were particularly useful in the interpretation of torsional rotational part of the problem. The applied reduced-axis-system (RAS) formalism allowed fitting within experimental accuracy the lines with K-a < 18. We also present the method of search for initial global solution of torsional rotational problem within RAS formalism. Accurate spectroscopic parameters obtained in this study provide a reliable basis for the detection of 4-hydroxy-2-butynenitrile in the interstellar medium.