In order to assess the quality of distorted videos accurately without reference videos, a universal no-reference video quality assessment algorithm is proposed, which applies three-dimensional (3D) convolutional neural networks to extracting spatiotemporal features of distorted videos. Firstly, the convolutional neural network model 3D ConvNets is trained on the video quality database, and then the features related to video distortion degree are learned. Then, 3D ConvNets is used to extract features of the input distorted video, after which L2-normalization and principal component analysis are performed to prevent overfitting and eliminate redundancy. Finally, linear support vector regression is used to predict quality score of the distorted video based on video quality features. The experimental results show that the proposed algorithm can assess video quality accurately across different kinds of distortion, and it still maintains a high level of accuracy when the test video database is changed. Last but not least, the computational complexity of quality assessment process is extremely low for the proposed algorithm.