As biological gender is one of the aspects of presenting individual human, much work has been done on gender classification based on people names. The proposals for English and Chinese languages are tremendous; still, there have been few works done for Vietnamese so far. We propose a new dataset for gender prediction based on Vietnamese names. This dataset comprises over 26,000 full names annotated with genders. This dataset is available on our website for research purposes. In addition, this paper describes six machine learning algorithms (Support Vector Machine, Multinomial Naive Bayes, Bernoulli Naive Bayes, Decision Tree, Random Forrest and Logistic Regression) and a deep learning model (LSTM) with fastText word embedding for gender prediction on Vietnamese names. We create a dataset and investigate the impact of each name component on detecting gender. As a result, the best F1-score that we have achieved is up to 96\% on LSTM model and we generate a web API based on our trained model.