High peak-to-average power ratio (PAPR) causes nonlinear impairments in intensity modulation direct detection (IM/DD) optical orthogonal frequency division multiplexing (O-OFDM) systems. Selective mapping (SLM) is a well-known effective PAPR reduction technique, but it suffers from high computational complexity due to the bank of inverse fast Fourier transforms (IFFTs) required to generate the set of candidate signals. In this paper, we propose a recombined SLM scheme that can generate up to 2U2 symbol candidates with U IFFTs. The candidate sequences are first partitioned and then recombined to generate new candidate signals, where the addition operation replaces the IFFT block and reduces the computational complexity significantly. Simulations and a real-time end-to-end IM/DD O-OFDM transmission system with line rate 10.5 Gb/s are set up to verify the performance of the proposed scheme. It is demonstrated that compared with conventional SLM, the proposed scheme achieves similar PAPR reduction performance with considerably lower computational complexity and no bit error rate degradation.