Logistic regression is a fast classifier and can achieve higher accuracy on small training data. Moreover,it can work on both discrete and continuous attributes with nonlinear patts. Based on these properties of logistic regression, this paper proposed an algorithm, called evolutionary logistical regression classifier (ELRClass), to solve the classification of evolving data streams. This algorithm applies logistic regression repeatedly to a sliding window of samples in order to update the existing classifier, to keep this classifier if its performance is deteriorated by the reason of bursting noise, or to construct a new classifier if a major concept drift is detected. The intensive experimental results demonstrate the effectiveness of this algorithm.