Oliver Stephenson was diagnosed with neuroblastoma, a rare type of cancer most commonly found in children under the age of five, last month.
He began treatment immediately, and has undergone three rounds of chemotherapy in less than four weeks.
His family have now launched a fundraiser which they hope will pay for further treatment in the USA.
Mum Laura, 34, said: “Oliver had his birthday on Boxing Day and we thought he looked tired.
“We took him to a doctor and they sent him for a blood test.
“We went for the test and that night I got a phone call from LGI. I took him in the following morning, the 15th of January. On the Friday he was diagnosed.
“There were no other signs at all, he was running around like a normal, healthy boy, but all the time he’d had stage four cancer.”
More than 2,000 people have joined a Facebook group where Laura provides updates on Oliver's treatment.
She thanked their friends and family for their support, which saw an initial fundraiser raise more than £10,000 to help Laura and her husband James, 32, with travel and expenses during Oliver’s treatment.
The couple have been able to take time off work to support Oliver and his brother Alfie, 2, during treatment.
But the family, from Ackworth, have now turned their attention to a larger fundraising goal, and hope to reach a total of £230,000 to allow them to pursue a clinical trial abroad.
The treatment, which is only available in the United States, is designed for patients in remission, and has been shown to help prevent a relapse.
If successful, Laura hopes that they will be able to take Oliver for treatment once he has completed his chemotherapy.
Laura said: “We’ve got to get through seven rounds of chemotherapy initially and the aim is that the chemo will get rid of all the cancer in his brain and his skull.
“If that works he’ll then have surgery and then an intensive four week blast of chemo.
“The Bradley Lowery foundation are willing to support us in raising money to go to America for a clinical trial.”
Visit www.justgiving.com/crowdfunding/oliverstephensonwillbeatthis for more information or to donate.