The results of a study on the binary HIP 18856 and construction of its orbit are presented. New observational data were obtained at the BTA of SAO RAS in 2007-2019. Earlier, Cvetković et al. constructed the orbit for this system. However, it is based on six measurements, which cover a small part of the orbit. The positional parameters of the ESA astrometric satellite Hipparcos published speckle interferometric data (Mason et al., Balega et al., Horch et al.) and new ones were used in this study. Based on the new orbital parameters, the mass sum was calculated and the physical parameters of the components were found. The obtained orbital and fundamental parameters were compared with the data from the study by Cvetković et al.. The comparison shows that the new orbital solution is better than the old one, since it fits new observational data accurately. Also based on a qualitative evaluation performed by Worley & Heintz, the new orbit was classified as “reliable”, which means data cover more than half of the orbit with sufficient quantities of residuals of measurements.