The gigahertz peaked spectrum (GPS) sources, compact steep spectrum (CSS) radio sources, and high-frequency peaker (HFP) radio sources are thought to be young radio active galactic nuclei (AGNs) at the early stage of AGN evolution. We investigated the optical properties of the largest sample of 126 young radio AGNs based on the spectra in SDSS DR12. We find that the black hole masses M_BH_ range from 10^7.32^ to 10^9.84^M_{sun}_ and the Eddington ratios R_edd_ vary from 10^-4.93^ to 10^0.37^, suggesting that young radio AGNs have various accretion activities and not all are accreting at high accretion rate. Our young radio sources generally follow the evolutionary trend towards large-scale radio galaxies with increasing linear size and decreasing accretion rate in the radio power-linear size diagram. The radio properties of low-luminosity young radio AGNs with low R_edd_ are discussed. The line width of [OIII]{lambda}5007 core ({sigma}[OIII]) is found to be a good surrogate of stellar velocity dispersion {sigma}*. The radio luminosity L_{5GHz}_ correlates strongly with [OIII] core luminosity L_[OIII]_, suggesting that radio activity and accretion are closely related in young radio sources. We find one object that can be defined as a narrow-line Seyfert 1 galaxy, representing a population of young AGNs with both young jet and early accretion activity. The optical variabilities of 15 quasars with multi-epoch spectroscopy were investigated. Our results show that the optical variability in young AGN quasars presents low variations (=<60 per cent) similar to the normal radio-quiet quasars.