Traditional methods of teaching music are largely subjective, with the lack of objectivity being particularly challenging for violin students learning vibrato because of the existence of conflicting theories. By using a computer-based analysis method, this study found that maintaining temporal coincidence between the intensity peak and the target frequency is the crucial factor for achieving good intonation when performing vibrato. This finding prompted the development of a computer-based visualised quantitative vibrato analysis system (VQVA-Sys) that displays these two parameters in a user-friendly manner for both musicians and scientists: (1) the type of frequency variation and (2) the corresponding frequencies with the highest intensities during all of the cycles constituting a vibrato note. A follow-up preliminary experimental investigation compared a moderately expressive vibrato note played by eight experts and eight students, and demonstrated the feasibility and potential usefulness of the VQVA-Sys as a learning tool.