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The chemical compositions of 26 metal-poor stars that exhibit strong CH and/or C 2 molecular bands are determined. Twenty-two stars in our sample satisfy our definition for carbon-enhanced metal-poor (CEMP) stars based on the carbon abundance ratio ([C/Fe]) and the evolutionary status. In addition, we measure Na abundances for nine known carbonenhanced stars. Combining our new sample with the results of previous work, we investigate the abundance and evolutionary status of a total of 64 CEMP stars. The following results are obtained: (1) All but one of the 37 stars with [Fe/H] ≥ -2.6 exhibit large excesses of barium ([Ba/Fe] < +0.5), while the other 27 stars with lower metallicity exhibit a large scatter in their barium abundance ratios (-1.2 < [Ba/Fe] < +3.3). (2) A correlation between the carbon and barium abundance ratios ([C/Fe] and [Ba/Fe]) is found in Ba-enhanced objects (comprising 54 stars), suggesting that the origin of the observed carbon excess in Ba-enhanced stars is nucleosynthesis in AGB stars, where the main s-process occurs. (3) The majority of the Ba-enhanced stars have -1.0 < [C/H] < 0.0, and a clear cutoff exists at [C/H] ∼ 0, which we take as the limit of carbon enrichment by metal-poor AGB stars. The [C/H] values of Ba-normal stars are relatively low, with a wide distribution. (4) The difference in the distributions of evolutionary status between Ba-enhanced and Ba-normal CEMP stars suggested by our previous work is not statistically confirmed by the present, enlarged sample. (5) Excesses of Na are found in stars with extremely large enhancements of C, N, and Ba, suggesting efficient production of this element by AGB nucleosynthesis. The implications of these results on the origins of carbon in CEMP stars are discussed.