The carrier frequency offset (CFO) on the orthogonal waveforms such as orthogonal frequency division multiplexing and offset quadrature amplitude modulation filter-bank multi-carrier (QAM-FBMC) has been well studied. However, the impact of the CFO on the QAM-FBMC systems is more complicated because of non-orthogonal prototype filters. The unavoidable interference from the non-orthogonality makes pilot signal design difficult and makes it hard to estimate the CFO accurately. In this paper, we discover the impact of the CFO on QAM-FBMC systems, evaluate the procedures of the basic CFO estimation methods, and analyze the performances of the CFO estimations. For the integer part estimation of CFO, we propose the design of pilot symbol that has a prominent peak at pilot subcarrier location in the up-sampled frequency domain. For the fractional part estimation, we formulate the basic CFO estimation by using two adjacent pilot symbols, and we analyze the mean-squared error performances with linear approximation and Cramer-Rao lower bound. We compare the performance of the CFO estimator and analytic approach in the additive white Gaussian noise and the pedestrian channel and show that the proposed estimator works well in the non-orthogonal QAM-FBMC systems.