Abstract: A fast algorithm is proposed to alleviate the time-consuming problem of the visible window calculation in multi-satellite and multi-target observation scenarios. This method decomposed the many-to-many observation problem into several one-to-one sub-problems, obtaining the surrounding suborbital track of each satellite to the observation target by R-tree indexing. Combining with the bisection method, the starting and ending time of the visible time window of the satellite to the observing target was determined. The simulation results of satellite observations for conical and rectangular fields of views show that: for visible time results with 1ms accuracy, the proposed algorithm obtains an average error around -8.5×10^-4 s compared with the STK (Satellite ToolKit) results. Compared with the tracking and propagation algorithm, it can reduce the computational redundancy by more than 99%, and the average time-consuming is 0.01% of the tracking and propagation algorithm with a step size of 1ms. The proposed algorithm can meet the accuracy and efficiency requirements of target observation window calculation in practical engineering applications.