Quality of experience (QoE) measures the overall perceived quality of mobile video delivery from subjective user experience and objective system performance. Current QoE prediction models have two main limitations: (1) insufficient consideration of the factors influencing QoE, and (2) limited studies on QoE models for acceptability prediction. In this paper, a set of novel acceptability-based QoE models, denoted as A-QoE, is proposed based on the results of comprehensive user studies on subjective quality acceptance assessments. The models are able to predict users' acceptability and pleasantness in various mobile video usage scenarios. Statistical nonlinear regression analysis has been used to build the models with a group of influencing factors as independent predictors, which include encoding parameters and bitrate, video content characteristics, and mobile device display resolution. The performance of the proposed A-QoE models has been compared with three well-known objective Video Quality Assessment metrics: PSNR, SSIM and VQM. The proposed A-QoE models have high prediction accuracy and usage flexibility. Future user-centred mobile video delivery systems can benefit from applying the proposed QoE-based management to optimize video coding and quality delivery strategies.