A significant number of transients in time-domain astronomy are discovered through multi-wavelength and multi-messenger observatories, posing a substantial challenge for the follow-up capabilities of astronomical observation satellites. To address this challenge, a modified adaptive large neighborhood search (MALNS) algorithm is developed to solve the astronomical observation satellite task scheduling problem (AOSTSP). The scheduling problem is formulated as a mathematical model incorporating time-dependent profits and transition times. Four destroy operators and four repair operators are introduced for the neighborhood search, with an adaptive strategy employed to select operators and update solutions during the optimization process. Within the MALNS framework, task selection is initially carried out, after which a heuristic task scheduling method is introduced. This method employs priority-based scheduling rules and a backpropagation adjustment mechanism to efficiently determine the start and end times of tasks, thereby maximizing profit while resolving conflicts. Experimental results demonstrate that the proposed method outperforms other approaches, such as the pure heuristic task scheduling algorithm and the particle swarm optimization algorithm, achieving the highest total profit and best overall performance in solving the AOSTSP.