In the next major phase of mobile telecommunications standards “5G,” Visible Light Communication (VLC) technology or light fidelity (Li-Fi) has great potential to be a breakthrough technology in the future of wireless Internet access. We propose a novel real-valued unipolar version of orthogonal frequency division multiplexing (OFDM) that is suitable for direct intensity modulation with direct detection (IM/DD) optical wireless systems including VLC. Without additional forms of interference estimation and cancelation to recover the symbols, the Spectral and Energy Efficient OFDM (SEE-OFDM) almost doubles the spectral efficiency of unipolar optical OFDM formats. In our scheme, multiple signals are generated and added/transmitted together, where both odd and even indexed subcarriers of the inverse fast Fourier transform (IFFT) operation carry data and are not affected by any kind of interference, (e.g., clipping). Monte Carlo simulations under additive white Gaussian noise (AWGN) show gains of up to 6dB in signal-to-noise ratio (SNR) compared to the conventional energy-efficient asymmetrically clipped optical OFDM (ACO-OFDM). Moreover, a peak-to-average power ratio (PAPR) reduction of 2.5dB is obtained as a bonus. Therefore, advantages such as increased data rate and reduced PAPR make the proposed SEE-OFDM very attractive for optical wireless systems.