The generalized linear spline model provides a convenient framework for the study of threshold effects and change-points for general outcomes, including binary and count outcomes. In this model, for a chosen link function, the effects of some factors of interest may change at change-points, also referred to as knots. In many applications, estimating and making inferences on change-points may be of primary interest. However, one often has to pre-specify the knots in fitting a generalized linear spline model due to the lack of rigorously studied and computational stable methods for knots estimation. We propose a simple and novel method for estimating the unknown knots as well as other parameters. Based on the idea of modified derivatives to overcome nondifferentiability of the model, a simple but non-regular estimating equation is proposed. A two-step semismooth Newton-Raphson algorithm is further proposed to solve this estimating equation. The statistical properties of this method is rigorously studied using the empirical process theory. Simulation studies have shown that the method performs well in terms of both statistical and computational properties.