The traditional graph-cut algorithm of video moving objects detection is based on the low-order Markov Random Field (MRF). Because of the low order approximation of the energy function, the detected moving objects will be over-smoothing. In this paper, an adaptive graph-cut algorithm based on Euler’s elastica model is proposed, which uses Euler’s elastica model to optimize the objects boundary and to amend the low-order approximation of the energy function. The proposed algorithm can continuously update the model parameters of current frame by Kalman prediction which estimates the number of moving objects pixels and objectives-background pixel-pairs. So the proposed algorithm can detect video moving objects in a continuous optimal mode. Experimental results show that the proposed method can effectively and stably detect moving objects, and the detection results can better meet the requirements of person's visual effects.