This paper proposes a power cost of mobility that is needed to compensate for fast fading. By the power cost of mobility we mean the additional SINR (signal-to-interference-plus-noise ratio) that is needed to meet the signal quality because the user is mobile. That is, the power cost of mobility in this paper is defined as the increment in power-control target SINR due to fast fading. We consider closed-loop power control (CLPC) based on SNR (signal-to-noise ratio) instead of SINR because it is difficult to analyze statistically power-controlled interference. The channel is modeled as flat Rayleigh fading. The probability density function (pdf) of the received SNR is derived in terms of the power control updating rate, maximum SNR, and Doppler frequency of the fading channel. In cellular systems with quadrature phase shift keying (QPSK) modulation, we study the power cost with various power control updating rates and Doppler frequencies of the fading channel.