Abstract-Recently proposed universal filtered multi-carrier (UFMC) system is not an orthogonal system in multipath channel environments and might cause significant performance loss. In this paper, we propose a cyclic prefix (CP) based UFMC system and first analyze the conditions for interference-free one-tap equalization in the absence of transceiver imperfections. Then the corresponding signal model and output SNR (signal-tonoise ratio) expression are derived. In the presence of carrier frequency offset (CFO), timing offset (TO) and insufficient CP length, we establish an analytical system model as a summation of desired signal, inter-symbol interference (ISI), intercarrier interference (ICI) and noise. New channel equalization algorithms are proposed based on the derived analytical signal model. Numerical results show that the derived model matches the simulation results precisely, and the proposed equalization algorithms improve the UFMC system performance in terms of bit error rate (BER).