In this paper, we consider the sequential spectrum sensing in a practice-matching cognitive raio (CR) scenario, where the primary user (PU) can operate under more than one transmit power levels as regulated in IEEE 802.11 Series, LTE, LTE-A, etc. In this case, the sensing targets not only include detecting the presence of PU but also include recognizing the transmit power level of PU. We propose two different sequential sensing schemes, i.e., detection before recognition and recognition before detection, and also derive the closed form decision regions. Performance of both schemes are compared. Numerical examples are then provided to corroborate the proposed studies.