Let p be an odd prime. The author investigates mod p-cohomology of the alternating group \(A_{p^ n}\). He exploits the fact that in this case the regular representation \(({\mathbb{Z}}/p)^ n\hookrightarrow S_{p^ n}\) in the symmetric group factors through the alternating group. A modification of earlier methods of Mui, Cooper and the author, developed for computation of cohomology of symmetric groups, gives a description of \(H^*(A_{p^ n};{\mathbb{Z}}/p)\).