With the development of speech synthesis technology, automatic speaker verification (ASV) systems have encountered the serious challenge of spoofing attacks. In order to improve the security of ASV systems, many antispoofing countermeasures have been developed. In the front-end domain, much research has been conducted on finding effective features which can distinguish spoofed speech from genuine speech and the published results show that dynamic acoustic features work more effectively than static ones. In the back-end domain, Gaussian mixture model (GMM) and deep neural networks (DNNs) are the two most popular types of classifiers used for spoofing detection. The log-likelihood ratios (LLRs) generated by the difference of human and spoofing log-likelihoods are used as spoofing detection scores. In this paper, we train a five-layer DNN spoofing detection classifier using dynamic acoustic features and propose a novel, simple scoring method only using human log-likelihoods (HLLs) for spoofing detection. We mathematically prove that the new HLL scoring method is more suitable for the spoofing detection task than the classical LLR scoring method, especially when the spoofing speech is very similar to the human speech. We extensively investigate the performance of five different dynamic filter bank-based cepstral features and constant Q cepstral coefficients (CQCC) in conjunction with the DNN-HLL method. The experimental results show that, compared to the GMM-LLR method, the DNN-HLL method is able to significantly improve the spoofing detection accuracy. Compared with the CQCC-based GMM-LLR baseline, the proposed DNN-HLL model reduces the average equal error rate of all attack types to 0.045%, thus exceeding the performance of previously published approaches for the ASVspoof 2015 Challenge task. Fusing the CQCC-based DNN-HLL spoofing detection system with ASV systems, the false acceptance rate on spoofing attacks can be reduced significantly.