In this paper we introduce the concept of congruences on hyper BCK-algebras and investigate the relationship between hyper BCK-ideals and those congruences. We show that If $\theta$ is a regular congruence on a hyper BCK-algebra $H$ then so $H/\theta$ is; There is a one-to-one correspondence between the set of all closed hyper BCK-ideals with condition (I*) and the set of all regular conguences with condition (C*); For any regular congruence $\vp$ on $H$, $\vp$ satisfies (C*) if and only if $H/\vp$ is a BCK-algebra.