We present VocalSet, a singing voice dataset of a capella singing. Existing singing voice datasets either do not capture a large range of vocal techniques, have very few singers, or are single-pitch and devoid of musical context. VocalSet captures not only a range of vowels, but also a diverse set of voices on many different vocal techniques, sung in contexts of scales, arpeggios, long tones, and excerpts. VocalSet has recordings of 10.1 hours of 20 professional singers (11 male, 9 female) performing 17 different different vocal techniques. This data will facilitate the development of new machine learning models for singer identification, vocal technique identification, singing generation and other related applications. To illustrate this, we establish baseline results on vocal technique classification and singer identification by training convolutional network classifiers on VocalSet to perform these tasks.