In direct sequence code division multi-access (DS-CDMA) mobile radio, closed-loop fast transmit power control (TPC) must be sufficiently fast to track fast multipath fading. However, in urban areas, the line-of-sight (LOS) path may appear abruptly when a mobile station comes out from behind a building and later suddenly the LOS may disappear, resulting in an abrupt path-loss change in the order of 30 to 40 dB. This "on-off" path loss change can be considered as a special case of shadowing. This rapid shadowing causes two problems at the base station: generation of large multiaccess interference (MAI) to other users when the LOS path appears and degradation in the quality of its own signal when the LOS path disappears. A new closed-loop fast TPC based on Markov-state transitions (called Markov fast TPC) is proposed. State transition is determined by the past history of the received binary TPC commands sent from the base station. The TPC step size is associated with the state. By changing the step size between as small as 0.8 dB and as large as 4 dB, the Markov fast TPC can better track rapid shadowing as well as multipath fading compared to conventional one-state closed-loop fast TPC. The TPC error is evaluated by computer simulation to demonstrate the adaptability of the proposed Markov fast TPC in a Rayleigh fading channel superimposed by LOS.