We present the detection of long-period RV variations in HD. 36384, HD. 52030, and HD. 208742 by using the high-resolution, fiber-fed Bohyunsan Observatory Echelle Spectrograph (BOES) for the precise radial velocity (RV) survey of about 200 northern circumpolar stars. Analyses of RV data, chromospheric activity indicators, and bisector variations spanning about five years suggest that the RV variations are compatible with planet or brown dwarf companions in Keplerian motion. However, HD. 36384 shows photometric variations with a period very close to that of RV variations as well as amplitude variations in the weighted wavelet Z-transform (WWZ) analysis, which argues that the RV variations in HD. 36384 are from the stellar pulsations. Assuming that the companion hypothesis is correct, HD. 52030 hosts a companion with minimum mass 13.3 M-Jup orbiting in 484 days at a distance of 1.2 au. HD. 208742 hosts a companion of 14.0 M-Jup at 1.5 au with a period of 602 days. All stars are located at the asymptotic giant branch (AGB) stage on the H-R diagram after undergoing. the helium flash and leaving. the giant clump. With stellar radii of 53.0 R-circle dot and 57.2 R-circle dot for HD. 52030 and HD. 208742, respectively, these stars may be the largest yet, in terms of stellar radius, found to host substellar companions. However, given possible RV amplitude variations and the fact that these are highly evolved stars, the planet hypothesis is not yet certain.