In this paper, we present a two-component Weibull mixture model. An important property is that this new model accommodates bimodality, which can appear in data representing phenomena in some heterogeneous populations. We provide some useful statistical properties, such as quantile function and moments. Also, the Expectation-Maximization (EM) algorithm used to find maximum-likelihood estimates of the model parameters is discussed. Further, a Monte Carlo study is carried out to evaluate the performance of the estimators on finite samples. The new model's relevance is shown with an application referring to vote proportion for the Brazilian presidential elections runoff in 2018. The proportion of votes is an important measure to analyze electoral data, and since it is a variable limited to the unitary interval, unit distributions should be considered to analyze its probabilistic behavior. Thus, the introduced model is suitable for describing the characteristics detected in these data, such as the asymmetric behavior, bimodality, and the unit interval as support. In the application, the superiority of the proposed model is verified when comparing the fit with the two-component beta mixture models.