In this paper, using the Mittag-Leffler-type Borel distribution, the authors introduce a new class of bi-Bazilevic functions defined in the open unit disc associated with Legendre polynomials, we find estimates for the general Taylor-Maclaurin coefficients of the functions in the subclass introduced, and the Fekete-Szego problem is solved. © 2022, International Scientific Research Publications All rights reserved.