In this paper, we introduce and characterize a core regular double MS-algebra. A construction of a core regular double MS-algebra M[2] via a de Morgan algebra M is given. A one to one correspondence between the class of de Morgan algebras and the class of core regular double MS-algebras is obtained. According to such construction we investigate many properties of a core regular double MS-algebra deal with subalgebras, homomorphisms, atoms and dual atoms. A description of an atomic core regular double MS-algebra is established. Also, we discuss some properties of a complete core regular double MS-algebra.