Recent work for extracting relations from texts has achieved excellent performance. However, most existing methods pay less attention to the efficiency, making it still challenging to quickly extract relations from massive or streaming text data in realistic scenarios. The main efficiency bottleneck is that these methods use a Transformer-based pre-trained language model for encoding, which heavily affects the training speed and inference speed. To address this issue, we propose a fast relation extraction model (FastRE) based on convolutional encoder and improved cascade binary tagging framework. Compared to previous work, FastRE employs several innovations to improve efficiency while also keeping promising performance. Concretely, FastRE adopts a novel convolutional encoder architecture combined with dilated convolution, gated unit and residual connection, which significantly reduces the computation cost of training and inference, while maintaining the satisfactory performance. Moreover, to improve the cascade binary tagging framework, FastRE first introduces a type-relation mapping mechanism to accelerate tagging efficiency and alleviate relation redundancy, and then utilizes a position-dependent adaptive thresholding strategy to obtain higher tagging accuracy and better model generalization. Experimental results demonstrate that FastRE is well balanced between efficiency and performance, and achieves 3-10$\times$ training speed, 7-15$\times$ inference speed faster, and 1/100 parameters compared to the state-of-the-art models, while the performance is still competitive. Our code is available at \url{https://github.com/seukgcode/FastRE}.