Flapping-wing MAVs are starting to emulate the advanced flight maneuverability of insects and birds, however they struggle to achieve a similar aptitude for taking off and landing in challenging cluttered environments. The ability to perch on objects such as branches or metal struts would result in a wide range of potential landing sites, both indoors and outdoors, and would increase the achievable mission duration, thus allowing a more versatile usage of MAVs. While perching is particularly challenging with flapping-wing MAVs, these vehicles are highly promising for complex missions in confined spaces. In this letter a systematic bioinspiration approach was adopted to design a new lightweight perching solution suitable for bird-size flapping-wing MAVs. The proposed concept combines a four-bar linkage mechanism with an active-passive actuation method to achieve a large gripping power at low energy consumption. Additionally it relies on compliant soft grippers inspired by the Fin Ray effect, which lead to a high adaptability to different perching surface textures and shapes. A prototype of the proposed concept was manufactured and tested experimentally in gripping tests and rail-guided perching tests. With a total mass of 45 g the concept is suited for bird-size MAVs in the weight range of 150–300 g. Flight tests on a surrogate (multirotor) platform demonstrate the approach functions successfully in realistic free-flight conditions.