The parent council of Anderston Primary, in Glasgow, has attacked moves to appoint an external candidate over current acting head Hazel Ralston, who has worked at the school for more than 20 years.
Members have written to officials at Glasgow City Council demanding the process be looked at again.
The letter from Elaine Daniels, chairwoman of the parent council, states: "We wish to raise our serious concerns about the process and are unhappy with the manner [of ]proceedings and the decision reached.
"At the interview, we, as the parent representatives on the panel, were unanimous in our decision to offer the vacant post to Hazel Ralston, who in our opinion was and is the most suitable candidate to take the school forward in a structured and forward-thinking fashion.
"We state this because we believe that her knowledge of the school, its staff, its catchment area, the pupils and their parents are unquestionably second to none and she commands the respect of staff, pupils and parents alike.
"We felt that our thoughts and wishes were ignored and counted for little on the day of the interview and we find it hard to accept that the decision was made by the casting vote of a chairperson who has little or no knowledge of the school, thus completely overruling the parents' wishes and views."
Ann Moran, secretary of Anderston Community Council, also attacked the decision in a letter to the council. She said: "I have been asked by the members of the council to express our utter dismay and disbelief at the apparent decision.
"Both the parents and the members are at a complete loss to understand why the so obviously perfect candidate for the position appears to have been overlooked."
Elizabeth Hendry, the new headteacher, is expected to meet parents from the school within a few days.
A council spokeswoman said the correct procedures had been followed.
She said: "The best candidate for the position of headteacher was appointed following the usual interview process and parents fully participated in the selection. It's deeply disappointing that parents now feel the need to question a decision that they agreed to at the time of the interviews."