In recent years, synthetic speech generated by advanced text-to-speech (TTS) and voice conversion (VC) systems has caused great harms to automatic speaker verification (ASV) systems, urging us to design a synthetic speech detection system to protect ASV systems. In this paper, we propose a new speech anti-spoofing model named ResWavegram-Resnet (RW-Resnet). The model contains two parts, Conv1D Resblocks and backbone Resnet34. The Conv1D Resblock is based on the Conv1D block with a residual connection. For the first part, we use the raw waveform as input and feed it to the stacked Conv1D Resblocks to get the ResWavegram. Compared with traditional methods, ResWavegram keeps all the information from the audio signal and has a stronger ability in extracting features. For the second part, the extracted features are fed to the backbone Resnet34 for the spoofed or bonafide decision. The ASVspoof2019 logical access (LA) corpus is used to evaluate our proposed RW-Resnet. Experimental results show that the RW-Resnet achieves better performance than other state-of-the-art anti-spoofing models, which illustrates its effectiveness in detecting synthetic speech attacks.