Recently, subsampling or refining images generated from unconditional GANs has been actively studied to improve the overall image quality. Unfortunately, these methods are often observed less effective or inefficient in handling conditional GANs (cGANs) -- conditioning on a class (aka class-conditional GANs) or a continuous variable (aka continuous cGANs or CcGANs). In this work, we introduce an effective and efficient subsampling scheme, named conditional density ratio-guided rejection sampling (cDR-RS), to sample high-quality images from cGANs. Specifically, we first develop a novel conditional density ratio estimation method, termed cDRE-F-cSP, by proposing the conditional Softplus (cSP) loss and an improved feature extraction mechanism. We then derive the error bound of a density ratio model trained with the cSP loss. Finally, we accept or reject a fake image in terms of its estimated conditional density ratio. A filtering scheme is also developed to increase fake images' label consistency without losing diversity when sampling from CcGANs. We extensively test the effectiveness and efficiency of cDR-RS in sampling from both class-conditional GANs and CcGANs on five benchmark datasets. When sampling from class-conditional GANs, cDR-RS outperforms modern state-of-the-art methods by a large margin (except DRE-F-SP+RS) in terms of effectiveness. Although the effectiveness of cDR-RS is often comparable to that of DRE-F-SP+RS, cDR-RS is substantially more efficient. When sampling from CcGANs, the superiority of cDR-RS is even more noticeable in terms of both effectiveness and efficiency. Notably, with the consumption of reasonable computational resources, cDR-RS can substantially reduce Label Score without decreasing the diversity of CcGAN-generated images, while other methods often need to trade much diversity for slightly improved Label Score.