Abstract: In this paper, we proved the existence of the solution to a backward stochastic differential equations (BSDE) with the generator satisfying the generalized left-Lipschitz condition. The key idea for dealing with the problem consists in constructing a monotonic sequence of solutions to BSDE and then passing to the
limit. We construct a monotonic sequence of solutions by monotonic iteration technique. It is worth noting that the generator may be not continuous with respect to variable yand the varying of generator with respect to variables y and z may be not uniformly with respect to time parameter t.

Key words: existence, generalized left-Lipschitz, existence