Abstract: The charge radius of an atomic nucleus describes its charge distribution, which is important for the understanding of the nucleon-nucleon interaction in medium. However, conventional physical models can not yet provide a satisfactory description of nuclear charge radii through-out the nuclear chart, especially for exotic phenomena such as the strong odd-even staggerings of the calcium isotopes. Recently, machine learning methods are widely applied to study various physical observables, such as nuclear charge radii. The applications of machine learning methods in studies of nuclear charge radii were briefly reviewed in this paper, including the naive Bayesian probability (NBP) classifier, kernel ridge regression (KRR) model, artificial neural network (ANN) and Bayesian neural network (BNN). In particular, the Bayesian neural network with six input features containing the relevant physical information, and a three-parameter phenomenological formula (NP formula) were combined to yield the so-called D6 model. It achieves a root-mean-square deviation (RMSD) between its predictions and the experimental data of 0.014 fm. It also yields the most accurate predictions for the charge radii of calcium isotopes, particularly the odd-even staggerings, which are in good agreement with the experimental data. The influence of different machine learning methods, training sets and input features on the predictions for nuclear charge radii, were compared in this work. Further applications of machine learning methods in nuclear physics are also commented.