Quantum Neural Network (QNN) combines the Deep Learning (DL) principle with the fundamental theory of quantum mechanics to achieve machine learning tasks with quantum acceleration. Recently, QNN systems have been found to manifest robustness issues similar to classical DL systems. There is an urgent need for ways to test their correctness and security. However, QNN systems differ significantly from traditional quantum software and classical DL systems, posing critical challenges for QNN testing. These challenges include the inapplicability of traditional quantum software testing methods to QNN systems due to differences in programming paradigms and decision logic representations, the dependence of quantum test sample generation on perturbation operators, and the absence of effective information in quantum neurons. In this paper, we propose QuanTest, a quantum entanglement-guided adversarial testing framework to uncover potential erroneous behaviors in QNN systems. We design a quantum entanglement adequacy criterion to quantify the entanglement acquired by the input quantum states from the QNN system, along with two similarity metrics to measure the proximity of generated quantum adversarial examples to the original inputs. Subsequently, QuanTest formulates the problem of generating test inputs that maximize the quantum entanglement adequacy and capture incorrect behaviors of the QNN system as a joint optimization problem and solves it in a gradient-based manner to generate quantum adversarial examples. Experimental results demonstrate that QuanTest possesses the capability to capture erroneous behaviors in QNN systems (generating 67.48%-96.05% more high-quality test samples than the random noise under the same perturbation size constraints). The entanglement-guided approach proves effective in adversarial testing, generating more adversarial examples (maximum increase reached 21.32%).