The potentials of massive multiple-input multiple-output (MIMO) are all based on the available instantaneous channel state information (CSI) at the base station (BS). Therefore, the user in frequency-division duplexing (FDD) systems has to keep on feeding back the CSI to the BS, thereby occupying large uplink transmission resources. Recently, deep learning (DL) has achieved great success in the CSI feedback. However, the existing works just focus on improving the feedback accuracy and ignore the effects on the following modules, e.g., beamforming (BF). In this paper, we propose a DL-based CSI feedback framework for BF design, called CsiFBnet. The key idea of the CsiFBnet is to maximize the BF performance gain rather than the feedback accuracy. We apply it to two representative scenarios: single- and multi-cell systems. The CsiFBnet-s in the single-cell system is based on the autoencoder architecture, where the encoder at the user compresses the CSI and the decoder at the BS generates the BF vector. The CsiFBnet-m in the multi-cell system has to feed back two kinds of CSI: the desired and the interfering CSI. The entire neural networks are trained by an unsupervised learning strategy. Simulation results show the great performance improvement and complexity reduction of the CsiFBnet compared with the conventional DL-based CSI feedback methods.