Fast and accurate MRI reconstruction is a key concern in modern clinical practice. Recently, numerous Deep-Learning methods have been proposed for MRI reconstruction, however, they usually fail to reconstruct sharp details from the subsampled $k$-space data. To solve this problem, we propose a lightweight and accurate Edge Attention MRI Reconstruction Network (EAMRI) to reconstruct images with edge guidance. Specifically, we design an efficient Edge Prediction Network to directly predict accurate edges from the blurred image. Meanwhile, we propose a novel Edge Attention Module (EAM) to guide the image reconstruction utilizing the extracted edge priors, as inspired by the popular self-attention mechanism. EAM first projects the input image and edges into ${\rm Q_{image}},$ ${\rm K_{edge}},$ and ${\rm V_{image}},$ respectively. Then EAM pairs the ${\rm Q_{image}}$ with ${\rm K_{edge}}$ along the channel dimension, such that 1) it can search globally for the high-frequency image features that are activated by the edge priors; 2) the overall computation burdens are largely reduced compared with the traditional spatial-wise attention. With the help of EAM, the predicted edge priors can effectively guide the model to reconstruct high-quality MR images with accurate edges. Extensive experiments show that our proposed EAMRI outperforms other methods with fewer parameters and can recover more accurate edges.