As one of the backend modules aboard the China Space Station Telescope, the high-sensitivity terahertz detection module (HSTDM) needs to be rationally scheduled to conduct various observation tasks to fulfill and maximize its scientific goals. This is because HSTDM cannot operate simultaneously with other modules, and the observable time windows determined by constrained and changeable conditions are randomly distributed and limited; even worse, the total allocated time is estimated to account for less than 10% of the total in-orbit time. We develop a modified genetic algorithm (MGA) to better solve this problem. Compared with conventional genetics algorithm (CGA), the core uniqueness of this method are as follows: (1) reduce the search space of chromosomes by pre-calculating the observable time windows of observing objects; (2) accelerate the exploration and exploitation of chromosomes by a transformation process that reduces the chromosome length through recombination of non-zero valued genes, followed by increasing the initial population diversity through the proposed similarity avoidance based population generation method and then by adopting stochastic universal sampling and elitism selection combined parents selection method; and (3) design a compound fitness function that can simultaneously achieve three optimization criteria through evolution process. The effectiveness of the proposed method is validated on a simulated scenario, and performance comparisons with CGA suggest that MGA can generate more profitable solutions (as much as 46% improvement) in fewer (as much as 90% reduction) generations.