This paper proposes an efficient algorithm for fast computation of the inverse real-valued discrete Fourier transform (IRDFT) using the decimation in frequency (DIF) approach. The proposed algorithm represents a direct method with a new implementation for fast computing of IRDFT. The algorithm derivation is based on the basic principles of the Cooley-Tukey algorithm with the divide and conquer approach and utilizes the advantage of conjugate symmetric property for the discrete Fourier transform (DFT) to remove all redundancies that appear when DFT deals with real data. The analyses of the proposed algorithm have shown that the arithmetic number has reached a minimum, therefore the structure of the developed algorithm possesses the desired properties such as regularity, simplicity, and in-place computation. The arithmetic complexity of this algorithm has been compared with the inverse FFT algorithm, and it was found that it needs the least number of multiplications and additions. The validity of the developed algorithm has been verified by reducing the peak-to-average power ratio PAPR in optical-OFDM systems compared with complex FFT. The simulation using MATLAB(R2021a) findings show that the RFFT O-OFDM system reduces PAPR more efficiently than the FFT O-OFDM system. The PAPR exhibits a reduction of approximately 2.4 to 2.75 dB when evaluated at a probability of occurrence of 10-1 in the complementary cumulative distribution function (CCDF) plot.