With the rapid development of intelligent Internet of Things (IoT) technology, many intensive computing workflow applications have been generated every day. Edge-cloud collaboration computing is a promising computational paradigm that combines the advantages of both edge and cloud to improve the application Quality of Service (QoS), shorten the time latency, and reduce the energy of the terminals. However, joining the heterogeneous resources for edge-cloud workflows efficiently and safely is still challenging. In this article, we develop an energy-aware and trust-collaboration cross-domain resource allocation (ETCRA) algorithm for edge-cloud workflows. The objective is to minimize the comprehensive system function (CSF) while guaranteeing the latency constraints of the workflows and trust constraints of the cross-domain edges. A dynamic algorithm is proposed to solve the formulated problem and to obtain the optimal task-resources mapping decision. It consists of two phases: 1) initial resource allocation decision making based on particle swarm optimization (PSO) statically and 2) real-time updating decision making based on the trust value assessment dynamically. Simulation results verify the effectiveness of ETCRA and prove that the proposed scheme significantly outperforms other baselines on four key measurements, including the CSF, total execution time, total energy consumption, and reliability performance.