Abstract: In order to improve the capability of cross-domain collaborative task scheduling of avionics systems in heterogeneous networking, a distributed cross-domain task scheduling method is proposed based on capability and task mapping in this paper. The concept of Mosaic warfare is employed to realize dynamic scheduling of resources according to task requirements. This method constructs perception subnets, decision subnets and response subnets for a complete task flow, and quantifies the capabilities of different subnets in a unified manner. The tasks are decomposed into sub-tasks, and sub-tasks are further decomposed into service requirements matching capabilities. In this way, the mapping between capabilities and service requirements is completed, and collaborative task scheduling is carried out in heterogeneous networking under the mapping conditions. In this paper, OMNeT++ simulation platform was used to compare the method with tactical data link and tactical cloud network. The simulation results show that compared with tactical cloud network architecture, the proposed method can improve packet throughput by 29.1%, reduce task group completion time by 36% on average, and reduce message transmission delay.