The spatial learned index constructs a spatial index by learning the spatial distribution, which performs a lower cost of storage and query than the spatial indices. The current update strategies of spatial learned indices can only solve limited updates at the cost of query performance. We propose a novel spatial learned index structure based on a Block Range Index (SLBRIN for short). Its core idea is to cooperate history range and current range to satisfy a fast spatial query and efficient index update simultaneously. SLBRIN deconstructs the update transaction into three parallel operations and optimizes them based on the temporal proximity of spatial distribution. SLBRIN also provides the spatial query strategy with the spatial learned index and spatial location code, including point query, range query and kNN query. Experiments on synthetic and real datasets demonstrate that SLBRIN clearly outperforms traditional spatial indices and state-of-the-art spatial learned indices in the cost of storage and query. Moreover, in the simulated real-time update scenario, SLBRIN has the faster and more stable query performance while satisfying efficient updates.