A synthetic spectrum-fitting analysis was applied to the Ca II line at 3933.68 A for 122 A-type stars (7000 <Te < 10000 K) in a wide range of rotational velocity (10 < vsini < 300 km/s), in order to study the behaviors of Ca abundances ([Ca/H]39) determined from this Ca II 3934 line, especially in context of (i) how they are related with the Am phenomenon (often seen in slow rotators) and (ii) whether they are consistent with the Ca abundances ([Ca/H]61) derived from the weaker Ca I 6162 line. It was confirmed that Ca line strengths in Am stars tend to be weaker and associated abundances are lower compared to non-Am stars at the same Te, indicating a deficiency of Ca in the photosphere of Am stars. However, an appreciable fraction of cool Am stars (Te < 8000 K) were found to show anomalous Ca II 3934 line feature (i.e., unusually broad for its weakness) which is hard to explain. Regarding the comparison between [Ca/H]39 and [Ca/H]61, while both are roughly consistent for hotter stars (Te > 8000 K), the former tends to be lower (by up to -1 dex or even more) than the latter for cooler A stars (Te < 8000 K) including those weak broad K line objects, This fact suggests that some special mechanism reducing the strength of Ca II 3934 line is involved at Te < 8000 K where [Ca/H]39 would be no more reliable. Whereas atomic diffusion causing the deficit of Ca in the photosphere as a result of element segregation in the deeper radiative envelope may be regarded as a promising explanation because it seems to fit in the qualitative trend of [Ca/H]61 in A-type stars, the well-known feature of considerably weak Ca II K line in classical Am stars should not necessarily be attributed to only this element diffusion scenario, for which some unknown weakening mechanism specific to this resonance line may independently be operative.