New CMOS imaging sensor (CIS) techniques in smartphones have helped user-generated content dominate our lives over traditional DSLRs. However, tiny sensor sizes and fixed focal lengths also lead to more grainy details, especially for zoom photos. Moreover, multi-frame stacking and post-sharpening algorithms would produce zigzag textures and over-sharpened appearances, for which traditional image-quality metrics may over-estimate. To solve this problem, a real-world zoom photo database is first constructed in this paper, which includes 900 tele-photos from 20 different mobile sensors and ISPs. Then we propose a novel no-reference zoom quality metric which incorporates the traditional estimation of sharpness and the concept of image naturalness. More specifically, for the measurement of image sharpness, we are the first to combine the total energy of the predicted gradient image with the entropy of the residual term under the framework of free-energy theory. To further compensate for the influence of over-sharpening effect and other artifacts, a set of model parameters of mean subtracted contrast normalized (MSCN) coefficients are utilized as the natural statistics representatives. Finally, these two measures are combined linearly. Experimental results on the zoom photo database demonstrate that our quality metric can achieve SROCC and PLCC over 0.91, while the performance of single sharpness or naturalness index is around 0.85. Moreover, compared with the best tested general-purpose and sharpness models, our zoom metric outperforms them by 0.072 and 0.064 in SROCC, respectively.