Oxfordshire County Council said out of 39 contracts supposed to be completed since 2013, 19 were finished on time.
This led to some schools using temporary classrooms and two had to postpone increases in pupil numbers until the following year.
Contractor Carillion blamed design changes and sub-contractors going bust.
At a recent cabinet meeting, Lorraine Lindsay-Gale, the councillor in charge of property, said: "Council is extremely concerned. We're working really hard with Carillion to try and improve matters".
In a statement the council added it: "Continues to be able to offer around nine out of 10 families in Oxfordshire a place at their first choice school, whether primary or secondary."
A Carillion spokesman said it "recognises the demands placed on schools by increases in pupil numbers" and continues to work "to provide the required additional space in schools".
"Where delays occurred, short term accommodation was provided until the work was completed."
A council has said it is "extremely concerned" over delays to school building projects that have forced some to turn down extra pupils.