The central value of an automorphic L-function plays a crucial role in number theory, as determining whether it vanishes or not can reveal profound arithmetic properties. The method of moments after Selberg and Iwaniec-Sarnak has been a powerful approach in showing positive proportions of non-vanishing central L-values in a family of L-functions. In this talk, we will establish asymptotic formulas for the twisted first and second moments of the central values for Mass forms over imaginary quadratic fields and deduce at least 33% central L-values are non-vanishing in this family. This is joint work with Zhi Qi.