Telford & Wrekin Green Party says it has organised the petition in response to local concerns and members will be setting up a stall in Wellington town centre on Saturday to collect signatures.
Party co-ordinator Patrick McCarthy says they are also calling for a review of existing services at Wellington Medical Practice.
He says there are concerns around access to face-to-face appointments with a GP and patients often struggle to get through on the phone.
Mr McCarthy, who lives in Wellington, says around 200 signatures have already been collected on a paper petition and online.
It will be delivered to Shropshire, Telford and Wrekin Clinical Commissioning Group, NHS England and Wellington Town Council.
Mr McCarthy said: "We are calling for another GP practice for Wellington and a review of the existing services.
"Wellington Medical Practice doesn't have the capacity to deal with the population.
"We also want them to organise a public meeting and talk to people about these issues."
The petition tears into the existing practice, saying: "We currently have a GP practice that reverses the public service ethos and makes everyone in our community feel that we are serving the needs of the practice rather than the other way around.
"Wellington Medical Practice are using the pandemic as an excuse for the appalling service they are delivering to our community."
The organisers also state: "Without adequate provision in the Wellington catchment area we fear for the safety of the most vulnerable members of our community.
"Wellington previously had two practices to serve this growing community but the second practice closed soon after it had opened due to the influx of disaffected patients transferring from the Wellington Practice.
"We demand that a second surgery is commissioned for the people of Wellington, better cited with accessibility."
Members of the local branch of the Green Party will be at a stall in Wellington town centre on Saturday between 11.30am and 2pm.
After Mr McCarthy raised concerns last month, a spokesperson from Wellington Medical Practice said it took them very seriously and staff had continued to work hard throughout the Covid-19 pandemic to deliver the best possible care for patients.
Shropshire, Telford and Wrekin Clinical Commissioning Group has been contacted for comment.