Is there a cure of gouty arthritis without using any medicines?

No cure. A natural anti-inflammatory is cherry extract can be purchased in capsule form..
Diet. Gout is caused by high levels of uric acid in the blood. Uric acid is produced in the body by breakdown of purines, nutrients found in high levels in foods like red meat, cheese, beer and wine. By avoiding these, you can lower your uric acid levels without using medicine. However, if gout is caused by kidney dysfunction, diet alone will not help. Talk to your primary doctor or a rheumatologist.
Not really. There are some herbal and homeopathic treatments, but I do not know how effective they are.
Permanent. There is a big difference between controlling gout and curing gouty arthritis. Controlling gout and the subsequent problems arising out of inadequately controlling it is hard enough, but once bony changes have occurred, all bets are off. There is no way of reversing the joint damage caused by uncontrolled gout. Some people may be able to rely on diet alone, but medications offer more success.