With the popularity of mobile Internet, audio and video (A/V) have become the main way for people to entertain and socialize daily. However, in order to reduce the cost of media storage and transmission, A/V signals will be compressed by service providers before they are transmitted to end-users, which inevitably causes distortions in the A/V signals and degrades the end-user's Quality of Experience (QoE). This motivates us to research the objective audio-visual quality assessment (AVQA). In the field of AVQA, most previous works only focus on single-mode audio or visual signals, which ignores that the perceptual quality of users depends on both audio and video signals. Therefore, we propose an objective AVQA architecture for multi-mode signals based on attentional neural networks. Specifically, we first utilize an attention prediction model to extract the salient regions of video frames. Then, a pre-trained convolutional neural network is used to extract short-time features of the salient regions and the corresponding audio signals. Next, the short-time features are fed into Gated Recurrent Unit (GRU) networks to model the temporal relationship between adjacent frames. Finally, the fully connected layers are utilized to fuse the temporal related features of A/V signals modeled by the GRU network into the final quality score. The proposed architecture is flexible and can be applied to both full-reference and no-reference AVQA. Experimental results on the LIVE-SJTU Database and UnB-AVC Database demonstrate that our model outperforms the state-of-the-art AVQA methods. The code of the proposed method will be publicly available to promote the development of the field of AVQA.