We present the results of a detailed high-resolution spectroscopic analysis (SUBARU/HDS spectra, R∼ 50000) of three faint high latitude carbon stars HE 1104–0957, HE 1205–0521, and HE 1244–3036. Our estimated metallicity for these objects is –2.96, –2.63 and –2.49, respectively. The surface chemical compositions of the objects are found to be characterized by enhanced carbon and heavy elements, such as Y, Ba, La, and Ce. Using the classification criteria for carbon-enhanced metal-poor (CEMP) stars the objects HE 1104–0957 and HE 1205–0521 could not be classified into any known CEMP sub-classes, whereas, the object HE 1244–3036 is found to be likely a CEMP-s star. The observed abundance patterns in HE 1244–3036 are also found to match well with the yields of a 2 M⊙ AGB star with [Fe/H] = –2.50. Although our kinematic analysis indicates that the objects belong to the halo population, the elemental abundance ratios of HE 1104–0957 and HE 1205–0521 do not match well with those of typical halo objects. Estimated elemental abundances are presented, and kinematic properties of the stars are discussed.