The new tables, published by Times Higher Education (THE), show Bristol placed just below Oxbridge, Sorbonne, Warwick and UCL when ranked on the quality of teaching (engagement, resources, outcomes and environment)
The rankings use the THE European Student Survey that accounts for about 50% of the overall placement.
Bristol ranked particularly highly on resources and student outcomes, after it emerged that Bristol graduates are amongst the highest paid in the country.
Bristol was in the top five in Europe of every single subject area apart from four, most of which are not offered at the University.
Professor Hugh Brady, Vice-Chancellor and President of the University of Bristol, said: “It is gratifying to see Bristol rank so highly in this new league table from the THE.
“It is also testament to the hard-word and dedication of our teaching staff in providing our students with the very best learning environments that are now ranked among some of the best in Europe.”