In this article, we introduce a new index transform associated with the cone function Pi√τ− 12 (2 √ x), named as Mehler-Fock-Clifford transform and study its some basic properties. Convolution and translation operators are defined and obtained their estimates under Lp(I; x− 12 dx) norm. The test function spaces Gα and Fα are introduced and discussed the continuity of the differential operator and MFC-transform on these spaces. Moreover, the pseudo-differential operator (p.d.o.) involving MFC-transform is defined and studied its continuity between Gα and Fα