This paper focuses on learning the representing dictionaries for sparse channel estimation in frequency-division duplexing (FDD) massive multiple-input multiple-output (MIMO) systems. To overcome the energy leakage problem in traditional sparse channel estimation, we propose a geographical dictionary- based spatial channel model to efficiently represent the cell-specific geographical characteristics. Based on that, the properties, especially the block structure, of the expected dictionaries are analyzed, and we design a data-driven joint block-structured dictionary learning algorithm (JBSDL) to obtain the expected representing dictionaries. The simulation environment is generated according to 3GPP standard, and we systematically study the properties of the learned dictionaries, which reveals the physical meaning of the dictionary learning results in massive MIMO systems. The proposed method demonstrates superior downlink channel estimation performance through the simulations.