Recent deep learning is superior in providing high-quality images and ultra-fast reconstructions in accelerated magnetic resonance imaging (MRI). Faithful coil sensitivity estimation is vital for MRI reconstruction. However, most deep learning methods still rely on pre-estimated sensitivity maps and ignore their inaccuracy, resulting in the significant quality degradation of reconstructed images. In this work, we propose a Joint Deep Sensitivity estimation and Image reconstruction network, called JDSI. During the image artifacts removal, it gradually provides more faithful sensitivity maps, leading to greatly improved image reconstructions. To understand the behavior of the network, the mutual promotion of sensitivity estimation and image reconstruction is revealed through the visualization of network intermediate results. Results on in vivo datasets and radiologist reader study demonstrate that, the proposed JDSI achieves the state-of-the-art performance visually and quantitatively, especially when the accelerated factor is high. Additionally, JDSI owns nice robustness to abnormal subjects and different number of autocalibration signals.