Our Lady of Lourdes Catholic Primary School in Bristol has lost all 16 of its tutors, including a head teacher and a newly qualified teacher, since the start of the year.
However, a spokesman for the local authority said the figure of 16 staff leaving over the year is "misleading" as it includes temporary staff who covered for people leaving mid-year.
A NUT spokeswoman said staff had complained that a "heavy-handed management style has caused so many teachers to be off with stress". She also added, "This rate of turnover is unacceptable. Children need consistency and stability. There should have been much stronger intervention once the situation was known."
NUT divisional secretary Karla Wheeler said in a statement: "To our knowledge, this is the first mass resignation in a South Gloucestershire school.
"We demand an urgent inquiry into what has happened in Our Lady of Lourdes Primary School - to learn the lessons, if nothing else.
"When the entire teaching staff of a school resigns, some of them before having jobs to go to, there is something wrong."
Her statement indicated what had caused the mass resignation.
She stated: "Our members have complained of an atmosphere of intimidation and unreasonable demands, which made some ill and which has caused a mass resignation."
Parents were told by governors this week that an entirely new teaching staff would be in place from September with a new head from the beginning of next year.