In this paper, we propose the problem of online cost-sensitive clas- sifier adaptation and the first algorithm to solve it. We assume we have a base classifier for a cost-sensitive classification problem, but it is trained with respect to a cost setting different to the desired one. Moreover, we also have some training data samples streaming to the algorithm one by one. The prob- lem is to adapt the given base classifier to the desired cost setting using the steaming training samples online. To solve this problem, we propose to learn a new classifier by adding an adaptation function to the base classifier, and update the adaptation function parameter according to the streaming data samples. Given a input data sample and the cost of misclassifying it, we up- date the adaptation function parameter by minimizing cost weighted hinge loss and respecting previous learned parameter simultaneously. The proposed algorithm is compared to both online and off-line cost-sensitive algorithms on two cost-sensitive classification problems, and the experiments show that it not only outperforms them one classification performances, but also requires significantly less running time.