For some time universities have warned they may have to close their teacher training departments as successive governments imposed ever greater demands.
But Liverpool is the first university to pull out voluntarily - having comfortably passed inspections by the Office for Standards in Education and the Teacher Training Agency.
Announcing the decision, vice-chancellor Philip Love said that with a comparatively small number of students the university had found it difficult to organise and fund the course.
The higher education sector has been critical of OFSTED inspections of teacher training courses - attacking both their frequency and approach.
Students must now spend much more time in schools, and institutions are also having to introduce basic literacy, numeracy and information technology tests for their trainees.
Liverpool's current cohort of 150 teacher trainees will be its last. A spokesman was unable to say how many staff would be affected by the axing of the primary and secondary courses. Subjects covered include the shortage areas of maths, science and modern languages.
The university will continue to offer in-service training and professional development courses for serving teachers, as well as pursuing research interests in the area.
Professor Love said: "While we fully support a mechanism for publicly assessing the quality of provision, we cannot continue to offer high-quality initial teacher training courses with a comparatively low volume of students.
"This university's experience demonstrated problems of scale which we were unable to overcome, but it is important to us that we are ceasing this activity as an academically successful and high-quality provider."
Mary Russell, secretary of the Universities' Council for the Education of Teachers, said virtually every higher education institution was looking at whether it was worth staying in teacher training.
She added: "The Liverpool decision is a great pity. It does bring home what we have been saying - that the present system is very expensive, and that the pressures of inspections, quality assessments, and all the other demands being made of institutions and schools are just horrendous."
Rosemary Feasey, chairwoman of the Association of Science Education, said:
"It's a huge blow. The Government can't afford to lose any providers, but it may be indicative of what's to come over the next few years. I suspect many other colleges are looking at pulling out."