•A diagnostic method for freight wagons hunting performance is proposed.•An evaluation indicator HC is utilized to describe the hunting stability.•The detection principle and performance validation through simulations and experiments.•The proposed method has been applied on practical railway engineering. Vehicle hunting instability can cause a great threat to the operational safety of freight wagons, which urgently requires condition monitoring. To address this challenge, an innovative diagnostic method is proposed by employing an indicator called Hunting Coefficient (HC) applied on a wayside hunting detection system (WHDS). Firstly, a diagnostic index HC is defined according to the vehicle hunting characteristics, specifically related to the wheelset lateral amplitude A and frequency f. Subsequently, an in-depth analysis on hunting stability is conducted and a mapping relationship between HC and the vehicle hunting state is established, validated through a rig test. Furthermore, building on the detection principle, a case analysis is performed to verify the feasibility of the proposed method applied on WHDS. This approach provides a means to conduct condition monitoring for freight wagons hunting instability, offering a crucial foundation for condition-based maintenance.