For a large class of switched systems with zeno phenomenon, classical observer cannot be applied directly since the terms leading to zeno phenomenon are not derivable. However in this paper, by assuming that these terms are integrable in the less restrictive way, we can define a new output, with which algebraic observer can then be adopted to estimate the states of the studied switched systems with zeno phenomenon. For simplicity, the main idea is explained via normal forms, while it can also be extended to generic switched systems.