what is the first country been a non-market economy country?

Answer 1

Hard to say... Almost every ancient empire used conscripted labor on a large scale and thus could be called a non-market economy. So I'd guess the first non-market economy was Sumer, but it is entirely possible there were civilizations in the Americas that got around to it before Sumer...

Answer 2

I disagree with the previous answer in the sense that there was some market economy in all ancient socieities. Peasant production, and before that hunting and gathering for family or tribal supply, may have been the dominant source of all consumption from time immemorial to the industrial revolution, but there has been some trading since time immemorial too. The only genuine attempts at non-market economies are those of Communist countries in historically recent times and Britain in wartime and other similar circs. I would offer as an answer the Paris Commune of 1870-1 but Paris is not a country. The 'real' answer therefore has to be the USSR after 1917.