Spectral efficiency and energy efficiency are two important performance indicators of satellite systems. The Quasi-Constant Envelope Orthogonal Frequency Division Multiplexing(QCE-OFDM) technique can achieve both high spectral efficiency and low peak-to-average power ratio(PAPR). Therefore, the QCE-OFDM technique is considered as a promising candidate multi-carrier technique for satellite systems. However, the Doppler effect will cause the carrier frequency offset(CFO), and the non-ideal oscillator will cause the carrier phase offset(CPO) in satellite systems. The CFO and CPO will further result in the bit-error-rate(BER) performance degradation. Hence, it is important to estimate and compensate the CFO and CPO. This paper analyzes the effects of both CFO and CPO in QCE-OFDM satellite systems. Furthermore, we propose a joint CFO and CPO estimation method based on the pilot symbols in the frequency domain. In addition, the optimal pilot symbol structure with different pilot overheads is designed according to the minimum Cramer-Rao bound(CRB) criterion. Simulation results show that the estimation accuracy of the proposed method is close to the CRB. Spectral efficiency and energy efficiency are two important performance indicators of satellite systems. The Quasi-Constant Envelope Orthogonal Frequency Division Multiplexing (QCE-OFDM) technique can achieve both high spectral efficiency and low peak-to- average power ratio (PAPR) However, the Doppler effect will cause the carrier frequency offset (CFO), and the non-ideal oscillator will cause the carrier phase offset (CPO) in satellite systems. The CFO and CPO will further result in the bit-error-rate (BER) performance degradation. Hence, it is important to estimate and compensate the CFO and CPO. This paper analyzes the effects of both CFO and CPO in QCE- OFDM, satellite systems. Further, we propose a joint CFO and CPO estimation method based on the pilot symbols in the frequency domain. In addition, the optimal pilot symbol structure with different pilot overheads is designed results to the minimum Cramer-Rao bound (CRB) criterion. Simulation results show that the estimation accuracy of the proposed method is close to the CRB.