East London NHS Foundation Trust gave Victoria Wasteney a written warning and suspended her for nine months, after she prayed with a Muslim colleague and gave her a book about Christianity.
The colleague accused her of harassment and bullying.
In April 2015, an Employment Tribunal ruled that the Trust did not discriminate against Miss Wasteney by disciplining her.
But in October a judge granted her permission to appeal.
Ms Wasteney claims she's been discriminated against because of her faith.
Speaking about the case, she said: "I conducted all my conversations with my colleague in a sensitive and appropriate way. I knew she was from a different faith background and I was respectful of that. I didn't force my beliefs on anyone at any point. Surely there should be room for mutual conversations about faith, where appropriate, in the workplace?
""A complaint was made against me by someone who left the job the following month and who did not attend the NHS trust's disciplinary hearing or the Employment Tribunal. Evidence from text messages shows that we had a friendly relationship. I believe that the complaint has been handled in the way that it has because I am a Christian.
Her case is being supported by the Christian Legal Centre.
Chief Executive Andrea Williams said: "Victoria has been punished and left out in the cold for being honest and open about her faith and this highlights an unhealthy trend.
"Do we want to be left with working environments where people are forced to hide their identity and the things that matter most to them? Such environments are detrimental to meaningful working relationships and ultimately to productivity."
The appeal gets underway on Friday in London.