Eva Omondi, an RCN NHS nurse based in Luton, is facing the £624 immigration surcharge fee six times, for her and her family members.
With visas lasting three years, she must find a total of more than £11,000 to have access to the health service.
"I don't think it's fair," Ms Omondi told ITV News.
Speaking amid the which has seen more than 18,000 people die in UK hospitals, she added: "They really need to look at this as an emergency and just take it off because it's even embarrassing for our government to sit down and make decisions on members of staff who are key to the nation."
The Royal College of Nursing has been calling for the surcharge to be scrapped.
It is thought some 153,000 non-EU residents in the United Kingdom are forced to pay the £400 annual charge to use the health service, a cost that will rise to £624 from October.
It means that NHS workers are effectively taxed twice to use the service, once before they are paid, and again in the form of the Immigration Health Surcharge.
In the Budget last month it was announced that the charge would rise by £224 a year, expanding to include EEA migrants from January 2021.
The charge is applicable to people on work and limited leave to remain visas in the UK, including dependents and must be paid in advance for the entire length of their visa duration, with no ability to defer payments.
For some, it can means payments into the thousands when paying for several dependents, a cost which is potentially crippling for those on starting salaries of up to £24,000 as a nurse.
Dr Chandra Kanneganti chair of the British International Doctors Association told ITV News "it doesn't seem fair that those who already pay tax and national insurance" are asked to pay twice.
"You will have seen the enormous contribution of the international healthcare workers to the NHS," he said.
"We have almost 16 to 17 doctors already dying, number of nurses have died, number of other healthcare workers have died who are from overseas have died in the line of duty...that is the kind of contribution international doctors and nurses and other healthcare workers are contributing to the NHS."
"It will be a very good will if the government can consider scrapping the NHS surcharge at least for NHS workers."
On Thursday morning, the government defended the charge saying it does not undermine the work done by overseas staff for the NHS.
Cabinet minister Brandon Lewis said the surcharge ensures everyone pays for the health service in a "fair and balanced" way, ensuring those who have not made lifelong contributions to the service are not able to benefit from the NHS without having to contribute.
He continued: "People who come here to work will more often than not do that for a limited period of time, the surcharge is around making sure they are giving something that is a fair balance between their ability to access it, as it is for all of us."
He added other countries around the world have the surcharge and that the UK is not alone in charging for this kind of access.
In a statement, the Home Office said: “We are immensely grateful for the work NHS doctors, nurses and paramedics are doing to tackle coronavirus, and this is why we applied a one-year visa extension to all those whose visas are due to expire before 1 October 2020 – this is completely free of charge and includes an exemption from the Immigration Health Surcharge.
“We will continue to look at whether we can provide further assistance during the fight against this virus.”