In the user-centric, cell-free, massive multi-input, multi-output (MIMO) orthogonal frequency division multiplexing (OFDM) system, a large number of deployed access points (APs) serve user equipment (UEs) simultaneously, using the same time–frequency resources, and the system is able to ensure fairness between each user; moreover, it is robust against fading caused by multi-path propagation. Existing studies assume that cell-free, massive MIMO is channel-hardened, the same as centralized massive MIMO, and these studies address power allocation and energy efficiency optimization based on the statistics information of each channel. In cell-free, massive MIMO systems, especially APs with only one antenna, the channel statistics information is not a complete substitute for the instantaneous channel state information (CSI) obtained via channel estimation. In this paper, we propose that energy efficiency is optimized by power allocation with instantaneous CSI in the user-centric, cell-free, massive MIMO-OFDM system, and we consider the effect of CSI exchanging between APs and the central processing unit. In addition, we design different resource block allocation schemes, so that user-centric, cell-free, massive MIMO-OFDM can support enhanced mobile broadband (eMBB) for high-speed communication and massive machine communication (mMTC) for massive device communication. The numerical results verify that the proposed energy efficiency optimization scheme, based on instantaneous CSI, outperforms the one with statistical information in both scenarios.