In this paper, we study the existence of the solution to one-dimensional forward–backward stochastic differential equations with neither the smooth condition nor the monotonicity condition for the coefficients. Under the nondegeneracy condition for the forward equation, we prove the existence of the solution to one-dimensional forward–backward stochastic differential equations. And we apply this result to establish the existence of the viscosity solution to a certain one-dimensional quasilinear parabolic partial differential equation