Nearly 70,000 calls to Avon and Somerset Police's non-emergency 101 helpline have not been answered quickly enough.
A Freedom of Information request made by the BBC has revealed an average of 70% of calls were answered within one minute between April and July 2014.
The force has a target of 85% of calls being answered within one minute.
The longest waiting time for a call to be answered was 49 minutes seven seconds in April.
'Improvements being made'
Assistant Chief Constable Kay Wozniak said they had 11,000 more calls in June and July this year, compared to the same months last year.
"I'd like to say sorry to any member of the public who has experienced delays getting through in the last few months to our 101 line," she said.
"I absolutely recognise it's not the service our public deserves and we have taken immediate action to improve this."
Police and Crime Commissioner (PCC) Sue Mountstevens said improvements are now being made with increased overtime and more staff in the force service centre.
"I can reassure residents these issues are being closely monitored by me and my team, and we are looking at this every day," she said.
Phone 'rang and rang'
Wendy Attridge from Wells, Somerset, took three attempts to get through to the 101 service in August, when she found a lost wallet.
"The first time I phoned it just rang and rang and rang, there were recorded messages and then it timed out; that was probably 10-15 minutes," she said.
"The second time it kept on ringing and I lost patience. Then I thought 'I really I need to get hold of them', and so on the third occasion I did get through quite quickly."
In July, when performance was well below targets, fewer than 55% of calls were answered within one minute.
July also had the highest rate of calls abandoned by callers who had waited more than one minute to be answered, at just under 9%, or 6,527 calls.
Between April 2013 and March 2014, 89% of calls were answered within one minute, but the target of 85% had not been met in any month between April and when the figures were collated on 20 August 2014.