Objective image quality assessment (IQA) aims to develop computational models to predict the perceptual image quality consistent with subjective evaluations. As image information is presented by the change in intensity values in the spatial domain, the gradient, as a basic tool for measuring the change, is widely used in IQA models. However, does the change measured by the gradient actually correspond to the change perceived by the human visual system (HVS)? To explore this issue, in this paper, we analyze how the ability of the HVS to perceive changes is affected by the upper threshold, and we propose an IQA index based on an adaptively truncating gradient. Specifically, the upper threshold at each pixel in an image is adaptively determined according to the image content, and the adaptively truncating gradient is obtained by retaining the part of the gradient magnitude that is less than the upper threshold and truncating the part that is greater than the upper threshold. Then, the distorted image quality is calculated by comparing the similarity of the adaptively truncating gradient between a reference image and the distorted image. Experimental results on six benchmark databases demonstrate that the proposed index correlates well with human evaluations.