Orthogonal frequency-division multiplexing (OFDM) communication is a promising technique for use in fourth-generation (4G) mobile communications. Meanwhile, the carrier aggregation technique becomes crucial for raising the transmission rate. The achievable data rate of an OFDM system is generally limited by spectral efficiency and the available bandwidth; the former strongly depends on the adopted modulation techniques, and the latter strongly depends on the spectrum policy. A carrier aggregation method is a feasible and flexible bandwidth utilization technique that facilitates upgrades to transmission throughput by aggregating several contiguous or non-contiguous carriers. Unlike conventional OFDM systems, multiple carrier frequency offsets (CFOs) must be taken into consideration for carrier-aggregated OFDM (CA-OFDM) communications. Several preambles are constructed as pilots for individual component carriers. With knowledge of the preamble property, novel estimation methods for multiple CFOs are proposed and investigated by taking advantage of either a multiple signal classification (MUSIC) or a root-MUSIC algorithm. Simulation results show that the proposed method can achieve good performance in terms of the error rate of detection and the mean-square error (MSE) over time-varying multipath fading channels. With assistance from the accurate multi-CFO estimation and compensation proposed in this paper, the carrier aggregation, which is conventionally accomplished on the medium access control (MAC) layer with a few parallel, ordinary OFDM inner receivers, can be effectively transformed to be a physical-layer (PHY) multiplexing technique by means of a larger-size fast Fourier transform (FFT) demodulation. This transformation can reduce the implementation overhead needed by independently building several parallel ordinary inner receivers. This transformation can also save the header length prefixed on the MAC layer for conducting carrier aggregations.