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Nonlinear effects between explanatory and response variables are increasingly present in new surveys.Here, we propose a flexible three-parameter semi-parametric cure rate survival based on theWeibull distribution. The proposed model is based on the generalized additive models for location, scale and shape,for which any or all parameters of the distribution are parametric linear and/or nonparametric smooth functions of explanatoryvariables. The new model is used to fit the nonlinear behavior between explanatory variables and cure rate.The flexibility of the proposed model is illustrated by predicting lifetime and cure rate proportionas well as identifying factors associated to women diagnosed with breast cancer.