In the context of wireless intelligent sensing and edge computing, a suitable way of modal parameter identification (MPI) for vibration monitoring of engineering structures is to use a distributed scheme where the majority of computing tasks are deployed to the sensor ends. This paper presents a time-domain algorithm called free-vibration-response based mode decomposition (FVRMD) for distributed MPI, which directly estimates frequency, damping ratio, initial amplitude, and initial phase from the vibration signals. Since FVRMD only relies on a single-channel input, it can be independently and synchronously deployed on each intelligent sensor in the distributed MPI scenario. Additionally, we provide a remote integration scheme to extract structure modal shape and the final representative frequency and damping ratio from the identified parameters at the edge. The proposed method is verified by analyzing vibrations in a simulated and experimental beam structure, as well as a real suspension bridge. Results demonstrate that the method is accurate and stable in estimating frequency and damping ratio, and its ability to identify modal shape is close to that of the centralized method. •A distributed modal parameters identification method based on FVRMD is provided.•It is good at damped signal decomposition and MPI with sound noise robustness.•The obtained modal shape is close to that obtained by the centralized method.•It is flexible to be deployed on distributed structural monitoring systems.