In this article, a new modulation scheme named Direct Current biased Optical Generalised Frequency Division Multiplexing (DCO-GFDM) for Visible Light Communications (VLC) is explored. The DCO-GFDM enhances spectral efficiency by slicing both grids on the time-frequency plane and uses a circularly rotating filter for pulse shaping. In the Circular Pulse shaped DCO-GFDM (CP-DCO-GFDM), Root Raised Cosine (RRC) pulse is widely employed. This destroys the orthogonality among sub-carriers and degrades the Bit Error Rate (BER) performance. Therefore, in this work, a Linearly Pulse shaped DCO-GFDM (LP-DCO-GFDM) is proposed to retain the orthogonality among the sub-carriers and simultaneously improve BER and Peak-to-Average Power Ratio (PAPR) performance. The performance of CP/LP-DCO-GFDM is studied under double sided clipping distortion that occurs at the Light Emitting Diode (LED). Presented simulation results agree well with the theoretical results. Additionally, we present an experimental validation of the LP-DCO-GFDM on a Universal Software Radio Peripherals (USRP) based VLC test bed. The experimental results, in terms of Error Vector Magnitudes (EVM)s, the received constellations, and the received spectrum in comparison with DCO-OFDM shows improved performance. © 2020 IEEE.