Mirfield Health Centre is considering adding two new rooms to the surgery to cope with demand.
On Tuesday Coun Alan Burton told Mirfield Town Council about a meeting he had with practice manager Milos Lukic.
This was in response to many Mirfield residents complaining that they cannot get appointments at the centre.
The lack of new GPs and traffic problems in Mirfield delaying doctors on call are two of the main reasons the service is stretched, Coun Burton told the meeting on Tuesday.
A new room is also nearly finished at the practice, which will make room for another doctor at the surgery.
Coun Burton said there were not enough young doctors wanting to go into general practice, with many opting to go down more lucrative areas of the profession. Traffic problems in the centre of the town also mean doctors are spending more time out of the surgery when on call than necessary.
Coun Burton also confirmed that no new patients were being taken from outside the Mirfield boundary.