Agile software development (ASD) methods were introduced as a reaction to traditional software development methods. Principles of these methods are different from traditional methods and so there are some different processes and activities in agile methods comparing to traditional methods. Thus ASD methods require different measurement practices comparing to traditional methods. Agile teams often do their projects in the simplest and most effective way so, measurement practices in agile methods are more important than traditional methods, because lack of appropriate and effective measurement practices, will increase risk of project. The aims of this paper are investigation on current measurement practices in ASD methods, collecting them together in one study and also reviewing agile version of Common Software Measurement International Consortium (COSMIC) publication.