Satellite communication systems, especially multi-beam low-Earth-orbit (LEO) satellites, could cater to the needs of different industrial applications through flexible resource allocation. Unfortunately, due to the wide coverage of LEO satellites, the data exchange within the LEO satellite networks suffers from the risk of eavesdropping and malicious jamming, which could severely degrade the performance of the industrial production process. To address such challenges, this paper introduces a multi-dimensional resource allocation strategy to facilitate covert communication within the multi-beam LEO satellite network. Our approach ensures the rate requirements of different user equipments while preventing the detection of communication signals by an eavesdropping geostationary orbit (GEO) satellite. Specifically, we formulate an optimization problem that jointly optimizes satellite beam-hopping scheduling, frequency band allocation, and the transmit power of different user equipments, under the covertness constraint. By introducing auxiliary binary variables, we transform this optimization problem into a Mixed-Integer Linear Programming (MILP) problem, which allows us to utilize machine learning-based techniques for efficient solution finding. The simulation results demonstrate the effectiveness of our proposed scheme.