This paper addresses observation task scheduling of a heterogeneous satellite constellation in low-Earth-orbits. The goal of scheduling is to find a sequence and times for observing the ground objects to maximize the sum of values of the observed ground objects while satisfying all the constraints associated with complex mission specifications. The method develops an instance of the asymmetric traveling salesman problem (ATSP) for this scheduling, and solves the resulting ATSP using a well-established Lin-Kernighan-Helsgaun algorithm. Numerical experiments demonstrate the characteristics, efficiency, and scalability of the proposed scheduling approach, in particular, compared to the first-in first-out strategy-based greedy algorithm.