An eccentric paddle locomotion mechanism (ePaddle) was proposed to enhance the mobility of amphibious robots for multi-terrains tasks. There are several feasible terrestrial and aquatic gaits for an ePaddle-based robot. In this paper, we present the method for modelling thrust in one of the aquatic gaits, namely the oscillating-paddling gait, for an ePaddle mechanism. The conception of the oscillating-paddling gait is introduced firstly and followed by the thrust model. In order to verify the proposed model, a thrust measuring facility is built. A series of experiments are carried out with this facility. From the results, we verify the thrust model for the oscillating-paddling gait. Furthermore, we characterize how the amplitude and direction of the generated net thrust force relate with the amplitude, period and oscillation ratio of the oscillating-paddling gait.