In a satellite communication (Sat-Com) system, channel coefficients from multiple-input, multiple-output (MIMO) antennas are correlated strongly because of a long propagation distance and a narrow angle spread. This is referred to as a keyhole (KH) channel, which results in a rank deficiency in the MIMO channel and a reduction in the number of simultaneously supportable multiple-access users. In addition, a high-power amplifier (HPA) in a satellite transponder distorts the transmitted signal due to its nonlinearity and memory. The aim of this paper is to study a satellite beamforming (BF) method and to investigate its signal-to-interference-plus-noise ratio (SINR) degradation due to the KH and HPA nonlinearity effects. A closed form of an optimum BF vector is not available due to HPA nonlinearity and memory, and a BF vector with simple complexity is desirable in practice. Therefore, this paper proposes a satellite transponder that uses column vectors from a discrete Fourier transform (DFT) matrix as precoding BF vectors in order for multiple ground terminals to meet their SINR demands.