Many researchers have recently acquainted and researched several interesting subfamilies of bi-univalent function family δ and they have found non-sharp estimates on the first two Taylor-Maclaurin coefficients |a_2 | and |a_3 |. In this current work, the subfamily F_(δ,q)^sc (α,Ξ) of bi-univalent functions in the sense of symmetric conjugate points with quasi subordination is defined. The Maclaurin coefficients |a_2 |, |a_3 | and besides related with these coefficients |a_3-〖a_2〗^2 | for functions belonging to this subfamily are derived. Further some corollaries are also presented.