Most maintenance strategies serving for the practical applications are formulated based on the single maintenance objective and do not consider the physical layout of compressor units in the complex pipeline networks and the actual maintenance demands, resulting in the over-maintenance or under-maintenance. The effective maintenance strategies for compressor units improve the unit reliability, economy, and maintenance efficiency. This work establishes a multi-level maintenance scheduling model composing of unit life prediction, unit-level maintenance decision, and system-level maintenance scheduling to guide the maintenance planning with cost and availability as the evaluation objectives. The maintenance strategies are developed by considering the series-parallel layout of compressor units, actual maintenance demands, and maintenance capability. The effectiveness of the proposed model is verified through 31 compressor unit networks in the Chinese west-east gas pipeline under the strategies of separating maintenance, combining maintenance, single maintenance team, and multiple maintenance teams, and compared it with the traditional methods. Compared with the traditional individual and simultaneous maintenance modes, the proposed method based on the optimal time window can reduce the maintenance cost by at least 27.7% and 25.1%, respectively. The weight factors and reliability have a great influence on the cost increase rate and unit availability. The multi-objective maintenance scheduling can improve the unit availability by 1.6% compared with the single availability optimization objective, and the corresponding maintenance cost rate is only increased by 0.68%. For the complex compressor unit networks, it is a better choice to consider the multi-objective maintenance planning under the single maintenance team. The model can improve the anti-risk ability of compressor units in long-distance natural gas networks and put forward maintenance suggestions from the perspective of safety, economy, and reliability.