Skou was born in 1918, in an ancient Danish town of Lemvig in a rich family of forest and coal miners. He graduated from Copenhagen University in 1944 and there he defended his thesis in 1954. Since 1947 Skou worked at the University of Aarhus.

In the early 1950s, Skow studied the mechanism of action of anesthetics. He found that the effect of anesthetic is due to his ability to dissolve in the lipid layer of the cell membrane and to overlap the sodium channels. Scowe suggested that the channel is a protein molecule and its blocking in neurons leads to the fact that nerve cells lose the ability to be excited, which leads to anesthesia. Skou also tried to isolate ATPhase from the crab nerve, but he did not succeed, and he continued other studies of anesthesia for a long time without realizing the enormous potential importance of this discovery. In 1958, at a conference in Vienna in the conversation with another researcher named Post, Skou learned about the finding of a cardiotoxic glycoside of uabain, an inhibitor of the sodium potassium pump. Using uabain, Skou quickly proved the connection between the enzyme ATPhase and the ion channel. 

Since 1988 he has been retired. In 1997, Skou received the Nobel Prize in Chemistry for the discovery of Na⁺ -K⁺ -ATPhase.