Activist Ewan McRobert said there were four primary schools in the Aberdeen area that were in this position.
He spoke out as members at the party’s Scottish conference in Dunfermline overwhelmingly backed a motion demanding an independent review of terms and conditions for the profession.
As well as calling for a wage hike for teachers, the Lib Dems want bonus payments for staff taking jobs in hard to fill areas, and higher salaries for headteachers, to encourage more applicants for such posts.
Mr McRobert said that “if teachers are the lifeblood of schools then head teachers are the beating hearts”.
But he told the conference: “In Aberdeen four primary schools have been trying to recruit a headteacher for three years.
“No, you didn’t mishear me. Some schools have languished without a headteacher for three years.”
He said that while Scottish teachers work “the second longest hours in the world” for the profession - behind only Colombia - a new teacher is paid 30% less than the average graduate salary of £30,000 a year.
“That is why it is urgent we increase teachers’ pay,” he said.
The Liberal Democrats are calling for an independent expert commission to review teachers’ terms and the demands placed upon them.
Education spokesman Tavish Scott said: “Teachers have had a rotten deal over recent years.
“They’ve been inundated with paperwork and diktats, lost thousands of teaching and pupil support colleagues, and been squeezed out of budgets.
“This plan shows Scottish Liberal Democrats are committing to restore the status, strength and resilience of the teaching profession.
“We’re bursting with good ideas to improve Scottish education, and the system is in sore need of them.
“Teachers are the backbone of Scottish education and they ought to command the pay and conditions to reflect that.”