Biffa was unveiled as North Somerset Council's waste collection provider in April 2017 but the service has been blighted with problems.
It has meant complaints about rubbish and recycling collections have doubled.
The company introduced new routes in May this year, but some households continued to have missed collections. Conservative Councillor Peter Bryant, who has responsibility for waste collection, apologised for the issues with the service in July.
However, the problems have not been fully resolved and figures obtained by the Liberal Democrats show Biffa has been issued with financial penalties 558 times between September 2017 and August 10 this year.
Many fines are for failing to collect bins, not providing photo evidence of blocked access and repeat missed collections.
Cllr Mike Bell said: "Since Biffa took over the contract last year, the performance levels have been really disappointing. We've had a long list of excuses from the council and Biffa reminiscent of the railway's 'leaves on the line'.
"Excuses over the past few months have included too much snow and cold weather, too much hot weather, poorly planned delivery routes inherited from the previous contractor, and badly planned re-routing by Biffa. We're now told a further re-routing is taking place which will get everything back on track.
"The massive increase in complaints and the poor service reported by residents has been allowed to drift for too long. The council needs to get to grips with this and be tougher with the contractor and get them to deliver the service they have promised. Taxpayers are forking out £7 million a year to Biffa through this contract and deserve a reliable and effective collection service. More than one year on, I fail to understand why this hasn't been sorted out."