Abstract: As the scale of available data increases, the importance and impact of machine learning grows. It has been found that quantum computing can be realized with the help of the principles of quantum mechanics, and the quantum machine learning algorithm formed by combining quantum computing and machine learning can theoretically produce exponential acceleration advantages over classical machine learning algorithms. Quantum versions of many classical algorithms have been proposed which may solve problems that are difficult to solve on classical computers. At present, limited by the quantum computing hardware, the number of controllable qubits, noise, and other factors restrict the development of quantum computers. Quantum computing hardware is unlikely to reach the level needed for universal quantum computers in the short term, and current research focuses on algorithms that can run on Noisy Intermediate-Scale Quantum (NISQ) computers. Variational quantum algorithms (VQAs) are hybrid quantum classical algorithms which are suitable for current quantum computing devices. Related research is one of the research hotspots in the field of quantum machine learning. Variational quantum circuits (VQCs) are parameterized quantum circuits (PQCs) used in variational quantum algorithms to solve quantum machine learning tasks. It is also be called Ansatz and quantum neural networks (QNNs). The framework of variational quantum algorithm mainly contains five steps: 1) Design the loss function according to the task. Design parameterized quantum circuits as model and initialize parameters. 2) Embed classical data. The classical data is pre-processed and encoded to the quantum state. If quantum data is used as input, it only needs to be pre-processed without encoding. 3) Calculate the loss function through parameterized quantum circuit. This step is where quantum advantage comes in. 4)Measure and post-process. Through quantum measurement operation, the quantum superposition state wave packet collapses into classical state. The classical data can be obtained after post-processing. 5) Optimize the parameters. Update parameters and optimize the model with classical optimization algorithms then return to step 3 until the loss function converges after several iterations. We can obtain a set of optimal parameters. The final result is the output of the optimal model. This paper reviews the basic theory of quantum computing and the basic framework of variational quantum algorithm. We further introduce the application and progress of variational quantum algorithm in the field of quantum machine learning. We review supervised quantum machine learning including quantum classifiers,unsupervised quantum machine learning including quantum circuit born machine,variational quantum boltzmann machine and quantum autoencoder, semi-supervised quantum learning including quantum generative adversarial network,quantum reinforcement learning, and quantum circuit architecture search in detail. We compare the models and analyse their advantages and disadvantages. We briefly discuss and summarize the related datasets and simulation platforms that can reproduce the introduced models. Finally, we put forward the challenges and future research trends of quantum machine learning algorithms based on variational quantum circuit.