Network topology obfuscation is generally considered as a promising proactive mechanism to mitigate traffic analysis attacks. The main challenge is to strike a balance among energy consumption, reliable routing, and security levels due to resource constraints in sensor nodes. Furthermore, software-defined Wireless Sensor Networks (WSNs) are more vulnerable to traffic analysis attacks due to the uncovered pattern of control traffic between the controller and the nodes. In this paper, a new energy-aware network topology obfuscation mechanism is proposed, which maximizes the attack costs and is efficient and practical to be deployed. Specifically, first, a route obfuscation method is proposed by utilizing ranking-based route mutation, based on four different critical criteria: route overlapping, energy consumption, link costs, and node reliability. Then, a sink node obfuscation method is introduced by selecting several fake sink nodes that are indistinguishable from actual sink nodes, according to the k-anonymity model. As a result, the most suitable routes and sink nodes can be selected, and a highest obfuscation level can be reached without sacrificing energy efficiency. Finally, extensive simulation results demonstrate that the proposed methods can strongly mitigate traffic analysis attacks and achieve effective network topology obfuscation for software-defined WSNs. In addition, the proposed methods can reduce the success rate of the attacks while achieving lower energy consumption and higher network lifetime.