Abstract: A ring is called(strongly)quasi J-*-clean ring if each of its elements is a sum of a quasi-projection and an element of the Jacobson radical(that commute). The basic properties of this ring and some relations with other rings are studied. It is proved that R is a strongly quasi J-*-clean ring if and only if R is a strongly *-clean ring and R/J(R) is a strongly quasi J-*-clean ring if and only if R/J(R) is a strongly quasi J-*-clean ring, every projection of R is central and every projection of R/J(R) is lifted to a projection of R.

Key words: clean ring, *-ring, quasi J-clean ring, quasi J-*-clean ring, strongly quasi J-*-clean ring