Testing Convolutional neural networks (CNNs) to find defects (e.g. error-inducing inputs) before deploying them in security-sensitive scenarios is crucial. Although existing white-box testing methods can effectively test CNN models with high coverage achieved, requiring full knowledge of target CNN models which may not always be available in privacy-sensitive scenarios. In this paper, we propose a novel Black-box Efficient Testing (BET) method for CNN models. The core insight of BET is that CNNs are generally prone to be affected by continuous perturbations. Thus, by generating such continuous perturbations in a black-box manner, we design a tunable objective function to guide our testing process for thoroughly exploring defects in different decision boundaries of target CNN models. We also design an efficiency-centric policy to find more error-inducing inputs with a fixed query budget. We conduct extensive evaluations with three well-known datasets and five popular CNN structures. The results show that BET significantly outperforms existing white-box or black-box testing methods considering the effective error-inducing inputs found in a fixed query/inference budget. We further show that the error-inducing inputs found by BET can be used to fine-tune the target model to improve the accuracy by up to 3%.