The answer to the question Is North Korea communist? depends to some extent on your definition of communism.
As most Americans understand communism, the answer is: Yes.
The North Korean government and Workers' Party of Korea (WPK, also known as the Korean Workers' Party) control most aspects of life, including major business entities. It calls itself a "socialist nation." The economy is centrally-planned.
More private "small business" has been tolerated in recent years, as the government's ability to provide employment and basics for its people has declined. Many people from all walks of life were forced to become "traders" to feed themselves and their families. This activity has sometimes been conducted under "gray market" conditions -- not legal, but tolerated by the authorities. However, North Korea has resisted pressure from China and other quarters to open up its economy in the Chinese mode, probably due at least in part to concerns by the leadership that such liberalization could lead it to lose control.
The North Korean government was created under the auspices of the Soviet Union as a communist nation. However, over time the North Koreans developed their own version of communism called Juche, which replaced traditional Marxist-Leninism. See more here. In recent years, the military has grown more powerful than the WPK. This is called songun, or the military-first policy, and is explained here.
Contrary to the theory of communism, the nation is ruled under a hereditary, cult of personality dictatorship; the current "Gen Y" dictator of Korea, Kim Jong Un (see more here), is the grandson of Kim Il Sung, the founder of North Korea.
Bottom line: North Korea is a communist dictatorship as that is commonly understood and a far stricter one than others such as China and Vietnam. That said, North Korea places great emphasis on its unique Korean-style of dictatorship.